Number of Terms 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 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 Progression [T_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.ⓘ Number of Terms of Arithmetic Progression given Sum of First N Terms [n]

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Number of Terms of Arithmetic Progression given Sum of First N Terms

Formula

`"n" = ((2*"S"_{"n"})/("a"+"T"_{"n"}))`

Example

`"15.87302"=((2*"500")/("3"+"60"))`

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Number of Terms of Arithmetic Progression given Sum of First N Terms Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
First Term of Progression - The First Term of Progression is the term at which the given Progression starts.
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.

STEP 1: Convert Input(s) to Base Unit

Sum of First N Terms of Progression: 500 --> No Conversion Required
First Term of Progression: 3 --> No Conversion Required
Nth Term of Progression: 60 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = ((2*S_n)/(a+T_n)) --> ((2*500)/(3+60))

Evaluating ... ...

n = 15.8730158730159

STEP 3: Convert Result to Output's Unit

15.8730158730159 --> No Conversion Required

FINAL ANSWER

15.8730158730159 ≈ 15.87302 <-- Index N of Progression

(Calculation completed in 00.004 seconds)

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< 4 Number of Terms in Arithmetic Progression Calculators

Number of Total Terms of Arithmetic Progression given Sum of Total Terms

Go Number of Total Terms of Progression = ((2*Sum of Total Terms of Progression)/(First Term of Progression+Last Term of Progression))

Number of Total Terms of Arithmetic Progression

Go Number of Total Terms of Progression = ((Last Term of Progression-First Term of Progression)/Common Difference of Progression)+1

Number of Terms of Arithmetic Progression given Sum of First N Terms

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

Number of Terms of Arithmetic Progression

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

Number of Terms of Arithmetic Progression given Sum of First N Terms Formula

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

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 Number of Terms of Arithmetic Progression given Sum of First N Terms?

Number of Terms of Arithmetic Progression given Sum of First N Terms calculator uses Index N of Progression = ((2*Sum of First N Terms of Progression)/(First Term of Progression+Nth Term of Progression)) to calculate the Index N of Progression, The Number of Terms of Arithmetic Progression given Sum of First N Terms formula is defined as the value of n for the nth term or the position of the nth term in an Arithmetic Progression, and calculated using the sum of first n terms of given Arithmetic Progression. Index N of Progression is denoted by n symbol.

How to calculate Number of Terms of Arithmetic Progression given Sum of First N Terms using this online calculator? To use this online calculator for Number of Terms of Arithmetic Progression given Sum of First N Terms, enter Sum of First N Terms of Progression (S_n), First Term of Progression (a) & Nth Term of Progression (T_n) and hit the calculate button. Here is how the Number of Terms of Arithmetic Progression given Sum of First N Terms calculation can be explained with given input values -> 50.79365 = ((2*500)/(3+60)).

FAQ

What is Number of Terms of Arithmetic Progression given Sum of First N Terms?

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

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

The Number of Terms of Arithmetic Progression given Sum of First N Terms formula is defined as the value of n for the nth term or the position of the nth term in an Arithmetic Progression, and calculated using the sum of first n terms of given Arithmetic Progression is calculated using Index N of Progression = ((2*Sum of First N Terms of Progression)/(First Term of Progression+Nth Term of Progression)). To calculate Number of Terms of Arithmetic Progression given Sum of First N Terms, you need Sum of First N Terms of Progression (S_n), First Term of Progression (a) & Nth Term of Progression (T_n). With our tool, you need to enter the respective value for Sum of First N Terms of Progression, First Term of Progression & Nth 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 Index N of Progression?

In this formula, Index N of Progression uses Sum of First N Terms of Progression, First Term of Progression & Nth Term of Progression. We can use 1 other way(s) to calculate the same, which is/are as follows -

Index N of Progression = ((Nth Term of Progression-First Term of Progression)/Common Difference of Progression)+1

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