Tiger Algebra/core — Serbian @ Weblate: An arithmetic sequence, or arithmetic progression, is a set of …

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An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. This difference is called the common difference. For example, all of the consecutive terms in the arithmetic sequence: 
<math>1, 4, 7, 10, 13, 16, 19, . . .</math> 
share a common difference of <math>3</math>. 
Note: The three dots (. . .) mean that this sequence is infinite. 

Though others can also be used, the following variables are typically used to represent the terms of an arithmetic sequence: 

<math>a_1</math> represents the first term of the sequence. In the example above, <math>a_1=1</math> 
<math>a_n</math> represents the nth term (a term we are trying to find). 
<math>d</math> represents the common difference between consecutive terms. In the example above, <math>d=3</math> 
<math>n</math> represents the number of terms in the sequence. In the example above, <math>n=7</math> 

The standard form of arithmetic sequences can be expressed as:
<math>a, a+d, a+2d, a+3d, a+4d, a+5d . . .</math> 
<math>a</math> represents the first term and is sometimes written as <math>a_1</math>. 
<math>d</math> represents the common difference. 

Formulas 
Finding any term (<math>a_n</math>) in an arithmetic sequence: 
<math>a_n=a+d(n-1)</math> 
<math>a\:</math> represents the first term. 
<math>d\:</math> represents the common difference. 
<math>n\:</math> represents the position of a term in the sequence. 
A sequence with <math>\:n\:</math> number of terms would be written as: 
<math>a, a+d(2-1), a+d(3-1), a+d(4-1), a+d(5-1), a+d(6-1) ... a+d(n-1)</math> 
in which the last term's common difference is multiplied by <math>\:n-1\:</math> (because <math>\:d\:</math> is not used in the 1st term). 
Example: To find the next term in: 
<math>1, 4, 7, 10, 13, 16, 19...</math> 
which would be the 8th term, we would plug the following into the general term formula <math>\:a_n= a+d(n-1)</math>: 

<math>a\:</math> (first term) <math> =1</math> 
<math>d\:</math> (common difference) <math> =3</math> 
<math>n\:</math> (term number) <math> =8</math> 
This would give us: 
<math>a_8=1+3(8-1)\:</math> which we could solve to get <math>\:a_8=22</math>. 
So, our sequence would be: <math>\:1, 4, 7, 10, 13, 16, 19, 22...</math> 

Finding the sum of all the terms in an arithmetic sequence: 
<math>s=n(a_1+a_n)/2</math> 
<math>s\:</math> is the sum of the terms in the sequence. 
<math>a\:</math> represents the first term. 
<math>n\:</math> represents the position of a term in the sequence. 
<math>d\:</math> represents the common difference. 

Example: To find the sum of: 
<math>1, 4, 7, 10, 13, 16, 19...\:</math> we plug the following into the sum formula <math>\:s=n(a_1+a_n)/2</math> : 

<math>n\:</math> (total number of terms)<math> =7</math> 
<math>a\:</math> (first term)<math> =1</math> 
<math>a_n\:</math> (the last term)<math> =19</math> 
This would give us: 
<math>s=7(1+19)/2\:</math> which we could solve to get <math>\:s=70</math>. 
So, the sum of the sequence would be: <math>\:70</math> 

Tiger identifies arithmetic sequences and displays their terms, the sum of their terms, and their explicit and recursive forms.

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Key	English	Serbian
ScientificNotationSolverStep1Title1NB1A10	Define the power of 10	Definiši stepen broja 10
ScientificNotationSolverStep1TextUnit1NB1A10	The absolute value of {Step1OriginalNumberNB1A10} is between 1 and 10, so the original number stays the same because the power of 10 is 1 and 0 is the exponent.	Apsolutna vrednost od {Step1OriginalNumberNB1A10} je između 1 i 10, tako da se prvobitni broj ne menja jer je stepen broja 10 jedan, a 0 je eksponent.
ScientificNotationSolverStep1TextUnit2NB1A10	{Step1OriginalNumberSolved1NB1A10}	{Step1OriginalNumberSolved1NB1A10}
ScientificNotationSolverStep2Title1NB1A10	Final result	Konačni rezultat
ScientificNotationSolverStep2TextUnit1NB1A10	{Step2FinalResultNB1A10}	{Step2FinalResultNB1A10}
ScientificNotationSolverFinalResultSpokenDescription	The final result is {SolutionFinalResult}	Konačni rezultat je {SolutionFinalResult}
AbsoluteValueEquations	Absolute value equations	Jednačine sa apsolutnim vrednostima
AbsoluteValueInequalities	Absolute value inequalities	Nejednačine sa apsolutnim vrednostima
AbsoluteValueEquationsContent	<h3>Absolute value</h3> Absolute value (sometimes called modulus or magnitude) is how far a number, term, polynomial, or expression is from zero, regardless of whether it is positive or negative. For example: <math>4</math> and <math>-4</math> are the same distance from <math>0</math>, so they both have an absolute value of <math>4</math>.<br><br> <img width="500" alt="Absolute value" src="https://user-images.githubusercontent.com/56831176/146247143-c8db661d-83ab-457f-9087-e9bc5cfa4ba3.png"><br> Absolute value is represented by two bars, one of each side of the number, term, polynomial, or expression. For example, the absolute value of <math>-4</math> would be written as <math>\|-4\|</math><br><br> <h3>Properties of absolute values</h3> <ul> <li>Non-negativity: <math>\|x\|≥0</math><br> Absolute value is always non-negative, meaning it <b>always</b> yields zero or a positive.</li><br> <li><math>\|x\|=\sqrt{x^2}</math>: Squaring a number makes it positive (or zero if the number is zero), and by taking the square root of a squared number we get a positive solution (or zero if the number is zero). This only works when <math>x</math> is a real number.</li><br> <li>Multiplicativity: <math>\|x\cdot y\|=\|x\|\cdot\|y\|</math><br> The absolute value of a product of two numbers equals the product of the absolute value of each number.</li><br> <li>Subadditivity: <math>\|x+y\|≤\|x\|+\|y\|</math><br> The absolute value of the sum of two real numbers is less than or equal to the sum of the absolute values of the two numbers.</li><br> <li><math>\|x\|=y → x=\pm y</math> or <math>\|x\|=\pm x</math>: If the absolute value of <math>x</math> equals <math>y</math> then <math>x</math> equals plus or minus <math>y</math>. This rule is used for solving most absolute value questions.</li> </ul> <br><br> <h3>Absolute value equations</h3> Absolute value equations are equations in which the variable is within an absolute value operator.<br> For example: <math>\|x-4\|=10</math><br> Because the value of <math>x-4</math> can be <math>10</math> or <math>-10</math>, both of which have an absolute value of <math>10</math>, we need to consider both cases: <math>x-4=10</math> and <math>x-4=-10</math>. This can also be written as <math>x-4=\pm10</math>.<br><br> So, <math>\|x-4\|=10</math> has two solutions:<br> <math>x-4=10</math> → <math>x=14</math><br> <math>x-4=-10</math> → <math>x=-6</math><br><br> Because absolute values are always non-negative, it is possible to have equations with no solutions.<br> For example: <math>\|x - 5\|=-9</math><br><br> Absolute Value Equations and Inequalities are solved and explained step by step by the Tiger Algebra Absolute Value module.	Apsolutna vrednost broja, prikazana između dve uspravne crte, može se posmatrati kao broj jedinica između nje i nule na brojevnoj pravi, bilo levo ili desno od nule, i uvek je pozitivan ceo broj. <br><br> Jednačine i nejednačine sa apsolutnim vrednostima rešavaju se i objašnjavaju postepeno u okviru Modula za apsolutne vrednosti na Tiger Algebra kalkulatoru.
AddingSubtractingFindingLeastCommonMultiple	Adding subtracting finding least common multiple	Sabiranje, oduzimanje, nalaženje najmanjeg zajedničkog sadržaoca
AddingSubtractingFindingLeastCommonMultipleContent	The Tiger Algebra Solver shows you how to add and subtract fractions and how to find their least common multiple for example:	Rešavač Tiger Algebra vam pokazuje kako da sabirate i oduzimate razlomke i kako da nađete njihov najmanji zajednički sadržalac, kao na primer:
ApproximationTopic	Approximation	Aproksimacija
Approximation	Approximation	Aproksimacija
ApproximationContent	Approximation in mathematics is defined as a quantity close in value to but not the same as a desired quantity. Two mathematical symbols denote approximate equality: a wavy equal sign (≈) and a dotted equal sign (≒ or ≓). <br><br> Approximation is often used when an precise form or integer is not known or easily obtainable as well as with irrational numbers, such as π. Approximation can turn a complex calculation, for example, involving decimals into one that uses integers, or whole numbers, making it easier to solve. This is achieved by rounding the decimal values before performing any further operations.	Aproksimacija se u matematici definiše kao kvantitet čija je vrednost približna, ali ne i jednaka vrednosti traženog kvantiteta. Dva matematička simbola označavaju približnu jednakost: talasasti znak jednakosti (≈) i znak jednakosti sa tačkama (≒ ili ≓). <br><br> Aproksimacija se često koristi onda kada nije poznat precizan oblik ili tačan celi broj ili se ne može lako dobiti, kao kod iracionalnih brojeva, kao što je π. Aproksimacija može da pretvori složeni proračun u koji su, na primer, uključene decimale, u proračun koji koristi cele brojeve, čime se olakšava rešavanje. Ovo se postiže zaokruživanjem decimalnih vrednosti pre izvođenja bilo koje sledeće operacije.
ArithmeticSequence	Arithmetic sequences	Aritmetički niz
ArithmeticSequenceContent	An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. This difference is called the common difference. For example, all of the consecutive terms in the arithmetic sequence:<br> <b><math>1, 4, 7, 10, 13, 16, 19, . . .</math></b><br> share a common difference of <math>3</math>.<br> Note: The three dots (. . .) mean that this sequence is infinite.<br><br> Though others can also be used, the following variables are typically used to represent the terms of an arithmetic sequence:<br> <math>a_1</math> represents the first term of the sequence. In the example above, <math>a_1=1</math><br> <math>a_n</math> represents the nth term (a term we are trying to find).<br> <math>d</math> represents the common difference between consecutive terms. In the example above, <math>d=3</math><br> <math>n</math> represents the number of terms in the sequence. In the example above, <math>n=7</math><br><br> The standard form of arithmetic sequences can be expressed as: <math>a, a+d, a+2d, a+3d, a+4d, a+5d . . .</math><br> <math>a</math> represents the first term and is sometimes written as <math>a_1</math>.<br> <math>d</math> represents the common difference.<br><br> <b>Formulas</b><br><br> <b>Finding any term (<math>a_n</math>) in an arithmetic sequence:</b><br> <b><math>a_n=a+d(n-1)</math></b><br><br> <math>a\:</math> represents the first term.<br> <math>d\:</math> represents the common difference.<br> <math>n\:</math> represents the position of a term in the sequence.<br> A sequence with <math>\:n\:</math> number of terms would be written as:<br> <math>a, a+d(2-1), a+d(3-1), a+d(4-1), a+d(5-1), a+d(6-1) ... a+d(n-1)</math><br> in which the last term's common difference is multiplied by <math>\:n-1\:</math> (because <math>\:d\:</math> is not used in the 1st term).<br><br> Example: To find the next term in:<br> <math>1, 4, 7, 10, 13, 16, 19...</math><br> which would be the 8th term, we would plug the following into the general term formula <math>\:a_n= a+d(n-1)</math>:<br> <math>a\:</math> (first term) <math> =1</math><br> <math>d\:</math> (common difference) <math> =3</math><br> <math>n\:</math> (term number) <math> =8</math><br> This would give us:<br> <math>a_8=1+3(8-1)\:</math> which we could solve to get <math>\:a_8=22</math>.<br> So, our sequence would be: <math>\:1, 4, 7, 10, 13, 16, 19, 22...</math><br><br> <b>Finding the sum of all the terms in an arithmetic sequence:</b><br> <b><math>s=n(a_1+a_n)/2</math></b><br><br> <math>s\:</math> is the sum of the terms in the sequence.<br> <math>a\:</math> represents the first term.<br> <math>n\:</math> represents the position of a term in the sequence.<br> <math>d\:</math> represents the common difference.<br> Example: To find the sum of:<br> <math>1, 4, 7, 10, 13, 16, 19...\:</math> we plug the following into the sum formula <math>\:s=n(a_1+a_n)/2</math> :<br> <math>n\:</math> (total number of terms)<math> =7</math><br> <math>a\:</math> (first term)<math> =1</math><br> <math>a_n\:</math> (the last term)<math> =19</math><br> This would give us:<br> <math>s=7(1+19)/2\:</math> which we could solve to get <math>\:s=70</math>.<br> So, the sum of the sequence would be: <math>\:70</math><br> Tiger identifies arithmetic sequences and displays their terms, the sum of their terms, and their explicit and recursive forms.	Aritmetički niz ili aritmetička progresija predstavlja niz brojeva kod kojih je razlika između uzastopnih članova (članova koji slede zaredom) konstantna. Na primer, između svih uzastopnih članova u aritmetičkom nizu:<br><b> 1, 4, 7, 10, 13, 16, 19, ...</b><br> zajednička razlika je 3.<br><br>Mada mogu da se koriste i neke druge, sledeće promenljive se obično koriste za predstavljanje članova aritmetičkog niza:<br> <b>a1</b> predstavlja prvi član niza<br> <b>an</b> predstavlja n-ti član (član koji pokušavamo da nađemo)<br> <b>d</b> predstavlja zajedničku razliku između uzastopnih članova<br> <b>n</b> predstavlja broj članova u nizu.<br><br>Tiger identifikuje aritmetičke nizove i prikazuje njihove članove, zbir njihovih članova i njihove eksplicitne i rekurzivne oblike.
BasicComplexOperations	Basic complex operations	Osnovne složene operacije
BasicComplexOperationsContent	A complex number is a number that can be expressed in the form <math>a + bi</math>, where a and b are real numbers and i is the imaginary unit, that satisfies the equation <math>x^2=−1</math>, that is, <math>i^2=−1</math>. In this expression, a is the real part and b is the imaginary part of the complex number. <br><br> The Tiger Algebra Calculator performs the basic operations on complex/imaginary numbers and shows you the step by step solution.	Kompleksan broj je broj koji se može predstaviti u obliku <math>a + bi</math>, gde su „a” i „b” realni brojevi, a „i” je imaginarna jedinica, što zadovoljava jednačinu <math>x^2=−1</math>, to jest, <math>i^2=−1</math>. U ovom izrazu, a je realni deo, a b je imaginarni deo kompleksnog broja. <br><br> Kalkulator Tiger Algebra izvršava osnovne operacije na kompleksnim/imaginarnim brojevima i pokazuje vam postepeno rešavanje problema.
CancelingOut	Canceling out	Skraćivanje razlomaka
CancelingOutContent	When simplifying fractions you can sometimes divide the top (NUMERATOR) and bottom (DENOMINATOR) of a fraction by the same number. This simplification of a fraction is referred to as canceling out/down . Common problems require you to write a fraction in its simplest terms. To achieve that, you must keep canceling the fraction until it cannot be cancelled anymore. <br><br> The Tiger Algebra Solver and Calculator can help you check your answers when canceling out.	Pri uprošćavanju razlomaka nekad možete istim brojem da podelite deo razlomka iznad (BROJILAC) i ispod razlomačke crte (IMENILAC). Ovo uprošćavanje razlomaka se zove skraćivanje. Kod uobičajenih problema potrebno je razlomak napisati pomoću najprostijih članova. Da biste to uspeli, potrebno je da skraćujete razlomak sve dok dalje skraćivanje više nije moguće. <br><br> Rešavač i Kalkulator Tiger Algebra mogu vam pomoći da proverite svoje odgovore pri skraćivanju.
CircleTopic	Circle from equation	Kružnica iz jednačine
CircleContent	In geometry, a circle is a shape made up of all the points on a plane at a fixed distance around a given point (the center). The equation for a circle is <math>(x-h)^2+(y-k)^2=r^2</math>, in which <math>h</math> and <math>k</math> represent the circle's center and <math>r</math> represents the circle's radius, the distance from the circle's center to any point on its perimeter. A circle with a center at <math>(4,5)</math> and a radius of <math>10</math>, for example, could be expressed as <math>(x-4)^2+(y-5)^2=100</math> <br> <img src="/images/circleImg1.png" alt="circle graph"> <br> <img src="/images/circleImg2.png" alt="circle related terms diameter, radius, chord, secant, tangent"> <br> <b>Relevant terms:</b><br> <ul> <li><b>Center</b>: The point around which a circle is formed. All points on a circle's perimeter are the same distance from the circle's center.</li><br> <li><b>Circumference</b>: The distance around a circle.</li><br> <li><b>Radius</b>: A line segment that lies between the center of a circle and any point on the circle's perimeter</li>.<br> <li><b>Diameter</b>: A line segment that lies between two points on a circle's perimeter and runs through the circle's center. It is equal to two times the circle's radius.</li><br> <li><b>Chord</b>: A line segment that lies between two points on a circle's perimeter and does not run through the circle's center.</li><br> <li><b>Secant</b>: A line that intersects two points on a circle's perimeter.</li><br> <li><b>Tangent</b>: A line that intersects one point on a circle's perimeter.</li> </ul>	U geometriji, kružnica je oblik sastavljen od svih tačaka na ravni na fiksnoj udaljenosti oko date tačke (središta). Jednačina za kružnicu je <mah>((x-h)^2)+((y-k)^2)=r^2</math>, u kojoj (h,k) predstavlja središte kružnice, a r predstavlja radijus kružnice, rastojanje od središta kružnice do bilo koje tačke na njenom obodu. Kružnica sa središtem na (4,5) i radijusom od 10 se može, na primer, izraziti kao </mah>((x-4)^2)+((y-5)^2)=100</math>. <br> <img src="/images/circleImg1.png" alt="circle graph"> <br> <img src="/images/circleImg2.png" alt="circle related terms diameter, radius, chord, secant, tangent"> <br> Važni pojmovi: <ul> <li>Središte: tačka oko koje se formira kružnica. Sve tačke na obodu kružnice su na istom rastojanju od središta kružnice.</li> <li>Opseg: rastojanje oko kružnice.</li> <li>Radijus: segment linije koji leži između središta kružnice i bilo koje tačke na obodu kružnice.</li> <li>Prečnik: segment koji leži između dve tačke na obodu kružnice i prolazi kroz središte kružnice. Jednako je dvostrukom radijusu kružnice.</li> <li>Tetiva: segment koji leži između dve tačke na obodu kružnice i ne prolazi kroz središte kružnice.</li> <li>Sekanta: prava koja seče dve tačke na obodu kružnice.</li> <li>Tangenta: prava koja seče jednu tačku na obodu kružnice.</li> </ul>
Combination	Combination	Kombinacija
CombinationTopic	Combination	Kombinacija
CombinationContent	In mathematics, a combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases it is possible to count the number of combinations. <br><br>Tiger Algebra calculates the number of combinations showing you the step by step solution. To activate, enter your input in one of the following forms: <div style="white-space: normal;"> <p>In combinatorics, a combination is a selection of items from a larger set, where the order of selection does not matter. Combinations are often used to count the number of ways to choose a subset of objects from a larger set.</p> <h2>Formula</h2> <p>The number of combinations of <math>k</math> items chosen from a set of <math>n</math> items (denoted as <math>C(n, k)</math> or <math>{n \choose k}</math>) is calculated using the combination formula:</p> <div style="margin-left: 20px;"> <math>C(n, k) = \frac{n!}{k!(n - k)!}</math>, </div> <p>where <math>n!</math> represents the factorial of <math>n</math>, defined as the product of all positive integers less than or equal to <math>n</math>.</p> <h2>Properties</h2> <ul> <li>The number of combinations is always a non-negative integer.</li> <li>Combinations are unordered, meaning that selecting the same set of items in a different order does not create a new combination.</li> <li>The number of combinations is often used in probability calculations and counting problems.</li> </ul> <h2>Example</h2> <p>Suppose we have a set of 5 letters: A, B, C, D, and E. We want to choose 3 letters from this set without regard to the order of selection. The number of possible combinations is:</p> <div style="margin-left: 20px;"> <math>C(5, 3) = \frac{5!}{3!(5 - 3)!} = \frac{5 \times 4 \times 3}{3 \times 2 \times 1} = 10</math>. </div> <p>Therefore, there are 10 different combinations of 3 letters that can be chosen from the set {A, B, C, D, E}.</p> <p>Combinations are fundamental in combinatorial mathematics and have numerous applications in various fields, including statistics, computer science, and cryptography.</p> </div>	U matematici, kombinacija predstavlja način izbora elemenata iz nekog skupa, takav da (za razliku od permutacija) redosled izbora nije važan. U manjem broju slučajeva moguće je izbrojati broj kombinacija. <br><br> Tiger Algebra izračunava broj kombinacija, pokazujući vam postepeno rešavanje problema. Da biste aktivirali, unesite svoje podatke u nekoj od sledećih formi:
DistanceBetweenTwoPointsAndTheirMidpoint	Distance between two points	Rastojanje između dve tačke i njihove središnje tačke
DistanceBetweenTwoPointsAndTheirMidpointContent	The distance formula, an application of the Pythagorean theorem, is a very helpful tool for finding the distance between two points. The Pythagorean theorem states the following: in a right triangle, the length of side <math>a</math> squared plus the length of side <math>b</math> squared is equal to the length of the hypotenuse (side <math>c</math>) squared.<br> <math>a^2+b^2=c^2</math><br> <img src="/images/distance-between-two-points-graph1.png" alt="Distance between two points graph"><br><br> The hypotenuse (<math>c</math>) is the longest side of a right triangle and is always opposite the right angle. The length of the hypotenuse also represents the distance between points <b>A</b> and <b>B</b>, which can each be represented by two coordinates: an <math>x</math> coordinate and a <math>y</math> coordinate.<br> Point <b>A</b> = <math>(x_1,y_1)</math><br> Point <b>B</b> = <math>(x_2,y_2)</math><br><br> To get the distance formula, we can rewrite the Pythagorean theorem as:<br> <math>d=\sqrt{(x_2−x_1)^2+(y_2−y_1)^2}</math><br> in which <math>d</math> represents the distance between points <b>A</b> and <b>B</b>, and the Xs and Ys represent the <math>x</math> and <math>y</math> coordinates of points <b>A</b> and <b>B</b>.<br><br> In order to find the distance between two points, enter their coordinates (for example (1,2) and (3,4)) and click the solve button.	Formula rastojanja, primena Pitagorine teoreme, vrlo je korisno sredstvo za pronalaženje rastojanja između dve tačke. Pitagorina teorema kaže sledeće: u pravouglom trouglu, dužina stranice <math>a</math> na kvadrat plus dužina stranice <math>b</math> na kvadrat jednaka je dužini hipotenuze (stranice <math>c</math>) na kvadrat.<br> <math>a^2+b^2=c^2</math><br> <img src="/images/distance-between-two-points-graph1.png" alt="Distance between two points graph"><br><br> Hipotenuza (<math>c</math>) je najduža stranica pravouglog trougla i uvek je nasuprot pravog ugla. Dužina hipotenuze takođe predstavlja rastojanje između tačaka <b>A</b> i <b>B</b>, od kojih svaka može biti predstavljena sa dve koordinate: <math>x</math> koordinatom i <math>y</math> koordinatom.<br> Tačka <b>A</b> = <math>(x_1,y_1)</math><br> Tačka <b>B</b> = <math>(x_2,y_2)</math><br><br> Da bismo dobili formulu rastojanja, možemo prepisati Pitagorinu teoremu kao:<br> <math>d=sqrt((x_2−x_1)^2+(y_2−y_1)^2)</math><br> u kojoj <math>d</math> predstavlja rastojanje između tačaka <b>A</b> i <b>B</b>, a Xs i Ys predstavljaju <math>x</math> i <math>y</math> koordinate tačaka <b>A</b> i <b>B</b>.<br><br> Da biste pronašli rastojanje između dve tačke, unesite njihove koordinate (na primer (1,2) i (3,4)) i kliknite na dugme za rešavanje.
DividingExponents	Dividing exponents	Deljenje eksponenata
DividingExponentsContent	<div style="white-space: normal;"> <p>When dividing expressions with exponents, you can use the properties of exponents to simplify the expression. Here's how:</p> <h2>Step 1: Subtract Exponents</h2> <p>To divide two terms with the same base, subtract the exponent of the divisor from the exponent of the dividend. For example, <math>x^a ÷ x^b = x^(a - b)</math>.</p> <p>For instance, if you have <math>x^5 ÷ x^2</math>, you subtract the exponents: <math>x^(5 - 2) = x^3</math>.</p> <h2>Step 2: Simplify</h2> <p>If there are additional terms in the expression, simplify them as well. For example, if you have <math>(x^5 * y^3) ÷ (x^2 * y)</math>, divide the x's and y's separately: <math>x^(5 - 2) * y^(3 - 1) = x^3 * y^2</math>.</p> <p>Remember, when dividing exponents with the same base, subtract the exponents.</p> <p>This process is crucial in algebra and higher-level mathematics when dealing with expressions containing exponents.</p> </div>	Rešavač Tiger Algebra vam pokazuje, korak po korak, kako da delite stepene. Na primer:
DividingFractions	Dividing fractions	Deljenje razlomaka
DividingFractionsContent	<div style="white-space: normal;"> <p>Dividing fractions is a fundamental operation in mathematics, especially in arithmetic and algebra. When dividing fractions, we follow specific rules to simplify the process and obtain the result.</p> <h2>Basic Concepts</h2> <p>To divide fractions, it's important to understand the following concepts:</p> <ul> <li><strong>Fractions:</strong> Numbers that represent parts of a whole or ratios of two quantities.</li> <li><strong>Dividing fractions:</strong> The process of dividing one fraction by another to find the quotient.</li> <li><strong>Reciprocal:</strong> The reciprocal of a fraction <math>\frac{a}{b}</math> is <math>\frac{b}{a}</math>.</li> </ul> <h2>Division Techniques</h2> <p>There are two common techniques to divide fractions:</p> <ul> <li><strong>Using reciprocals:</strong> Multiply the first fraction by the reciprocal of the second fraction.</li> <li><strong>Converting to multiplication:</strong> Convert the division operation to multiplication by multiplying the first fraction by the reciprocal of the second fraction.</li> </ul> <h2>Examples</h2> <p>Let's consider a few examples to illustrate the division of fractions:</p> <h3>Example 1:</h3> <p>Divide <math>\frac{3}{4}</math> by <math>\frac{1}{2}</math></p> <p>Using the reciprocal technique, we multiply the first fraction by the reciprocal of the second fraction:</p> <p><math>\frac{3}{4} \div \frac{1}{2} = \frac{3}{4} \times 2 = \frac{6}{4}</math></p> <p>Since <math>\frac{6}{4}</math> can be simplified to <math>\frac{3}{2}</math>, the result is <math>\frac{3}{2}</math>.</p> <h3>Example 2:</h3> <p>Divide <math>\frac{5}{8}</math> by <math>\frac{2}{3}</math></p> <p>We convert the division operation to multiplication by multiplying the first fraction by the reciprocal of the second fraction:</p> <p><math>\frac{5}{8} \div \frac{2}{3} = \frac{5}{8} \times \frac{3}{2}</math></p> <p>After simplification, we get the result as <math>\frac{15}{16}</math>.</p> <h2>Conclusion</h2> <p>Dividing fractions is a fundamental operation that plays a crucial role in various mathematical contexts. Mastering the techniques of fraction division enables efficient problem-solving and enhances mathematical understanding.</p> </div>	Kalkulator Tiger Algebra deli razlomke, pokazujući vam korak po korak kako se dolazi do rešenja. Na primer:

Key	English	Serbian
AltDisclosureIcon	Disclosure Icon	Ikona za pojašnjenje
AlternateForm	Alternative approach	Alternativni pristup
AltHandwritingIcon	Handwritting Icon	Ikona za rukopis
AltKeyboardIcon	Keyboard Icon	Ikona tastature
AltLogoIcon	Logo Icon	Logo ikona
AltMoreIcon	More Icon	Ikona za više
AltNativeKeyboardIcon	keyboard	tastatura
AltPlayIcon	Play Icon	Ikona za reprodukciju
AltSentFeedbackIcon	Sent Feedback Icon	Ikona za poslate povratne informacije
AltShareIcon	Share Icon	Ikona za deljenje
Approximation	Approximation	Aproksimacija
ApproximationContent	Approximation in mathematics is defined as a quantity close in value to but not the same as a desired quantity. Two mathematical symbols denote approximate equality: a wavy equal sign (≈) and a dotted equal sign (≒ or ≓). <br><br> Approximation is often used when an precise form or integer is not known or easily obtainable as well as with irrational numbers, such as π. Approximation can turn a complex calculation, for example, involving decimals into one that uses integers, or whole numbers, making it easier to solve. This is achieved by rounding the decimal values before performing any further operations.	Aproksimacija se u matematici definiše kao kvantitet čija je vrednost približna, ali ne i jednaka vrednosti traženog kvantiteta. Dva matematička simbola označavaju približnu jednakost: talasasti znak jednakosti (≈) i znak jednakosti sa tačkama (≒ ili ≓). <br><br> Aproksimacija se često koristi onda kada nije poznat precizan oblik ili tačan celi broj ili se ne može lako dobiti, kao kod iracionalnih brojeva, kao što je π. Aproksimacija može da pretvori složeni proračun u koji su, na primer, uključene decimale, u proračun koji koristi cele brojeve, čime se olakšava rešavanje. Ovo se postiže zaokruživanjem decimalnih vrednosti pre izvođenja bilo koje sledeće operacije.
ApproximationTopic	Approximation	Aproksimacija
ArithmeticMean	Arithmetic mean (Simple Average)	Aritmetička sredina (jednostavan prosek)
ArithmeticSequence	Arithmetic sequences	Aritmetički niz
ArithmeticSequenceContent	An arithmetic sequence, or arithmetic progression, is a set of numbers in which the difference between consecutive terms (terms that come after one another) is constant. This difference is called the common difference. For example, all of the consecutive terms in the arithmetic sequence:<br> <b><math>1, 4, 7, 10, 13, 16, 19, . . .</math></b><br> share a common difference of <math>3</math>.<br> Note: The three dots (. . .) mean that this sequence is infinite.<br><br> Though others can also be used, the following variables are typically used to represent the terms of an arithmetic sequence:<br> <math>a_1</math> represents the first term of the sequence. In the example above, <math>a_1=1</math><br> <math>a_n</math> represents the nth term (a term we are trying to find).<br> <math>d</math> represents the common difference between consecutive terms. In the example above, <math>d=3</math><br> <math>n</math> represents the number of terms in the sequence. In the example above, <math>n=7</math><br><br> The standard form of arithmetic sequences can be expressed as: <math>a, a+d, a+2d, a+3d, a+4d, a+5d . . .</math><br> <math>a</math> represents the first term and is sometimes written as <math>a_1</math>.<br> <math>d</math> represents the common difference.<br><br> <b>Formulas</b><br><br> <b>Finding any term (<math>a_n</math>) in an arithmetic sequence:</b><br> <b><math>a_n=a+d(n-1)</math></b><br><br> <math>a\:</math> represents the first term.<br> <math>d\:</math> represents the common difference.<br> <math>n\:</math> represents the position of a term in the sequence.<br> A sequence with <math>\:n\:</math> number of terms would be written as:<br> <math>a, a+d(2-1), a+d(3-1), a+d(4-1), a+d(5-1), a+d(6-1) ... a+d(n-1)</math><br> in which the last term's common difference is multiplied by <math>\:n-1\:</math> (because <math>\:d\:</math> is not used in the 1st term).<br><br> Example: To find the next term in:<br> <math>1, 4, 7, 10, 13, 16, 19...</math><br> which would be the 8th term, we would plug the following into the general term formula <math>\:a_n= a+d(n-1)</math>:<br> <math>a\:</math> (first term) <math> =1</math><br> <math>d\:</math> (common difference) <math> =3</math><br> <math>n\:</math> (term number) <math> =8</math><br> This would give us:<br> <math>a_8=1+3(8-1)\:</math> which we could solve to get <math>\:a_8=22</math>.<br> So, our sequence would be: <math>\:1, 4, 7, 10, 13, 16, 19, 22...</math><br><br> <b>Finding the sum of all the terms in an arithmetic sequence:</b><br> <b><math>s=n(a_1+a_n)/2</math></b><br><br> <math>s\:</math> is the sum of the terms in the sequence.<br> <math>a\:</math> represents the first term.<br> <math>n\:</math> represents the position of a term in the sequence.<br> <math>d\:</math> represents the common difference.<br> Example: To find the sum of:<br> <math>1, 4, 7, 10, 13, 16, 19...\:</math> we plug the following into the sum formula <math>\:s=n(a_1+a_n)/2</math> :<br> <math>n\:</math> (total number of terms)<math> =7</math><br> <math>a\:</math> (first term)<math> =1</math><br> <math>a_n\:</math> (the last term)<math> =19</math><br> This would give us:<br> <math>s=7(1+19)/2\:</math> which we could solve to get <math>\:s=70</math>.<br> So, the sum of the sequence would be: <math>\:70</math><br> Tiger identifies arithmetic sequences and displays their terms, the sum of their terms, and their explicit and recursive forms.	Aritmetički niz ili aritmetička progresija predstavlja niz brojeva kod kojih je razlika između uzastopnih članova (članova koji slede zaredom) konstantna. Na primer, između svih uzastopnih članova u aritmetičkom nizu:<br><b> 1, 4, 7, 10, 13, 16, 19, ...</b><br> zajednička razlika je 3.<br><br>Mada mogu da se koriste i neke druge, sledeće promenljive se obično koriste za predstavljanje članova aritmetičkog niza:<br> <b>a1</b> predstavlja prvi član niza<br> <b>an</b> predstavlja n-ti član (član koji pokušavamo da nađemo)<br> <b>d</b> predstavlja zajedničku razliku između uzastopnih članova<br> <b>n</b> predstavlja broj članova u nizu.<br><br>Tiger identifikuje aritmetičke nizove i prikazuje njihove članove, zbir njihovih članova i njihove eksplicitne i rekurzivne oblike.
ArithmeticSequenceResultType1	The common difference equals:	Zajednička razlika jednaka je:
ArithmeticSequenceResultType2	The sum of the sequence equals:	Zbir niza jednak je:
ArithmeticSequenceResultType3	The explicit formula of this sequence is:	Eksplicitna formula ovog niza je:
ArithmeticSequenceResultType4	The recursive formula of this sequence is:	Rekurzivna formula ovog niza je:
ArithmeticSequenceResultType5	The nth terms:	nth članovi:
ArithmeticSequenceSolver	Arithmetic sequences	Aritmetički nizovi
ArithmeticSequenceSolver.plugin	arithmetic sequences	aritmetički nizovi
ArithmeticSequenceStep1TextUnit1	Find the common difference by subtracting any term in the sequence from the term that comes after it.	Pronađi zajedničku razliku oduzimanjem bilo kog člana u nizu članova koji dolazi posle njega.
ArithmeticSequenceStep1TextUnit2	The difference of the sequence is constant and equals the difference between two consecutive terms.<br>{Step1Difference}	Razlika niza je konstantna i jednaka je razlici između dva uzastopna člana.<br>Korak1 {Step1Difference}
ArithmeticSequenceStep1Title	Find the common difference	Pronađi zajedničku razliku
ArithmeticSequenceStep2NT1	Plug in the terms.	Unesi članove
ArithmeticSequenceStep2NT2	Simplify the expression.	Pojednostavi izraz.
ArithmeticSequenceStep2TextUnit1	Calculate the sum of the sequence using the sum formula:	Izračunaj zbir niza koristeći formulu za zbir.
ArithmeticSequenceStep2TextUnit2	<span class="formula-look"><math>Sum=(n(a_1+a_n))/2</math></span>	<math>Zbir=(n(a_1+an))/2</math>

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Aritmetički niz ili aritmetička progresija predstavlja niz brojeva kod kojih je razlika između uzastopnih članova (članova koji slede zaredom) konstantna. Na primer, između svih uzastopnih članova u aritmetičkom nizu: 1, 4, 7, 10, 13, 16, 19, ... zajednička razlika je 3. Mada mogu da se koriste i neke druge, sledeće promenljive se obično koriste za predstavljanje članova aritmetičkog niza: 
a1 predstavlja prvi član niza 
an predstavlja n-ti član (član koji pokušavamo da nađemo) 
d predstavlja zajedničku razliku između uzastopnih članova 
n predstavlja broj članova u nizu. Tiger identifikuje aritmetičke nizove i prikazuje njihove članove, zbir njihovih članova i njihove eksplicitne i rekurzivne oblike.

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ArithmeticSequenceContent

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core/TigerAlgebra.Localization/Resources/TigerSharedResource.sr.resx, string 436