Nth Term of Arithmetic Progression given Sum of First N Terms Calculator

✖The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression.ⓘ Sum of First N Terms of Progression [S_n]			+10% -10%
✖The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.ⓘ Index N of Progression [n]			+10% -10%
✖The First Term of Progression is the term at which the given Progression starts.ⓘ First Term of Progression [a]			+10% -10%

✖The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.ⓘ Nth Term of Arithmetic Progression given Sum of First N Terms [T_n]

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Nth Term of Arithmetic Progression given Sum of First N Terms Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression
T_n = ((2*S_n)/n)-a
This formula uses 4 Variables

Variables Used

Nth Term of Progression - The Nth Term of Progression is the term corresponding to the index or position n from the beginning in the given Progression.
Sum of First N Terms of Progression - The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression.
Index N of Progression - The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.

STEP 1: Convert Input(s) to Base Unit

Sum of First N Terms of Progression: 500 --> No Conversion Required
Index N of Progression: 6 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_n = ((2*S_n)/n)-a --> ((2*500)/6)-3

Evaluating ... ...

T_n = 163.666666666667

STEP 3: Convert Result to Output's Unit

163.666666666667 --> No Conversion Required

FINAL ANSWER

163.666666666667 ≈ 163.6667 <-- Nth Term of Progression

(Calculation completed in 00.004 seconds)

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< Nth Term of Arithmetic Progression Calculators

Nth Term of Arithmetic Progression given Pth and Qth Terms

LaTeX Go Nth Term of Progression = ((Pth Term of Progression*(Index Q of Progression-1)-Qth Term of Progression*(Index P of Progression-1))/(Index Q of Progression-Index P of Progression))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression))

Nth Term from End of Arithmetic Progression

LaTeX Go Nth Term from End of Progression = First Term of Progression+(Number of Total Terms of Progression-Index N of Progression)*Common Difference of Progression

Nth Term of Arithmetic Progression given Sum of First N Terms

LaTeX Go Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression

Nth Term of Arithmetic Progression

LaTeX Go Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression

Nth Term of Arithmetic Progression given Sum of First N Terms Formula

LaTeX Go

Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression
T_n = ((2*S_n)/n)-a

What is an Arithmetic Progression?

An Arithmetic Progression or simply AP is a sequence of numbers such that successive terms are obtained by adding a constant number to the first term. That fixed number is called the common difference of the Arithmetic Progression. For example, the sequence 2, 5, 8, 11, 14,... is an Arithmetic Progression with first term is 2 and common difference is 3. An AP is a convergent sequence if and only if the common difference is 0, otherwise an AP is always divergent.

How to Calculate Nth Term of Arithmetic Progression given Sum of First N Terms?

Nth Term of Arithmetic Progression given Sum of First N Terms calculator uses Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression to calculate the Nth Term of Progression, The Nth Term of Arithmetic Progression given Sum of First N Terms formula is defined the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, and calculated using the sum of first n terms of given Arithmetic Progression. Nth Term of Progression is denoted by T_n symbol.

How to calculate Nth Term of Arithmetic Progression given Sum of First N Terms using this online calculator? To use this online calculator for Nth Term of Arithmetic Progression given Sum of First N Terms, enter Sum of First N Terms of Progression (S_n), Index N of Progression (n) & First Term of Progression (a) and hit the calculate button. Here is how the Nth Term of Arithmetic Progression given Sum of First N Terms calculation can be explained with given input values -> 530.3333 = ((2*500)/6)-3.

FAQ

What is Nth Term of Arithmetic Progression given Sum of First N Terms?

The Nth Term of Arithmetic Progression given Sum of First N Terms formula is defined the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, and calculated using the sum of first n terms of given Arithmetic Progression and is represented as T_n = ((2*S_n)/n)-a or Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression. The Sum of First N Terms of Progression is the summation of the terms starting from the first to the nth term of given Progression, The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression & The First Term of Progression is the term at which the given Progression starts.

How to calculate Nth Term of Arithmetic Progression given Sum of First N Terms?

The Nth Term of Arithmetic Progression given Sum of First N Terms formula is defined the term corresponding to the index or position n from the beginning in the given Arithmetic Progression, and calculated using the sum of first n terms of given Arithmetic Progression is calculated using Nth Term of Progression = ((2*Sum of First N Terms of Progression)/Index N of Progression)-First Term of Progression. To calculate Nth Term of Arithmetic Progression given Sum of First N Terms, you need Sum of First N Terms of Progression (S_n), Index N of Progression (n) & First Term of Progression (a). With our tool, you need to enter the respective value for Sum of First N Terms of Progression, Index N of Progression & First Term of Progression and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Nth Term of Progression?

In this formula, Nth Term of Progression uses Sum of First N Terms of Progression, Index N of Progression & First Term of Progression. We can use 3 other way(s) to calculate the same, which is/are as follows -

Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*Common Difference of Progression
Nth Term of Progression = ((Pth Term of Progression*(Index Q of Progression-1)-Qth Term of Progression*(Index P of Progression-1))/(Index Q of Progression-Index P of Progression))+(Index N of Progression-1)*((Qth Term of Progression-Pth Term of Progression)/(Index Q of Progression-Index P of Progression))
Nth Term of Progression = First Term of Progression+(Index N of Progression-1)*((Last Term of Progression-First Term of Progression)/(Number of Total Terms of Progression-1))

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