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

GoNumber of Terms of Arithmetic Progression Formula

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The Index N of Progression is the value of n for the nth term or the position of the nth term in a Progression. Check FAQs

n = (\frac{2 \cdot S n}{a + T n})

n - Index N of Progression?S_n - Sum of First N Terms of Progression?a - First Term of Progression?T_n - Nth Term of Progression?

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

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Here is how the Number of Terms of Arithmetic Progression given Sum of First N Terms equation looks like with Values.

Here is how the Number of Terms of Arithmetic Progression given Sum of First N Terms equation looks like with Units.

Here is how the Number of Terms of Arithmetic Progression given Sum of First N Terms equation looks like.

15.873 = (\frac{2 \cdot 500}{3 + 60})

15.873 = (\frac{2 \cdot 500}{3 + 60})

15.873 = (\frac{2 \cdot 500}{3 + 60})

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

Follow our step by step solution on how to calculate Number of Terms of Arithmetic Progression given Sum of First N Terms?

FIRST Step Consider the formula

n = (\frac{2 \cdot S n}{a + T n})

Next Step Substitute values of Variables

∴

n = (\frac{2 \cdot 500}{3 + 60})

Next Step Prepare to Evaluate

∴

n = (\frac{2 \cdot 500}{3 + 60})

Next Step Evaluate

∴

n = 15.8730158730159

LAST Step Rounding Answer

∴

n = 15.873

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

Variables

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.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Index N of 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.

Symbol: S_n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Sum of First N Terms of Progression

First Term of Progression

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

Symbol: a

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find First Term of Progression

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.

Symbol: T_n

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Nth Term of Progression

Credits

Created by Nayana Phulphagar

Institute of Chartered and Financial Analysts of India National college (ICFAI National College), HUBLI

Nayana Phulphagar has created this Formula and 300+ more formulas!

Verified by Nikita Salampuria

The National Institute of Engineering (NIE), Mysuru

Nikita Salampuria has verified this Formula and 600+ more formulas!

Other Formulas to find Index N of Progression

Go Number of Terms of Arithmetic Progression

n = (\frac{T n - a}{d}) + 1

Other formulas in Number of Terms in Arithmetic Progression category

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

n Total = (\frac{2 \cdot S Total}{a + l})

Go Number of Total Terms of Arithmetic Progression

n Total = (\frac{l - a}{d}) + 1

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

Number of Terms of Arithmetic Progression given Sum of First N Terms evaluator uses Index N of Progression = ((2*Sum of First N Terms of Progression)/(First Term of Progression+Nth Term of Progression)) to evaluate 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 evaluate Number of Terms of Arithmetic Progression given Sum of First N Terms using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Number of Terms of Arithmetic Progression given Sum of First N Terms?

The formula of Number of Terms of Arithmetic Progression given Sum of First N Terms is expressed as Index N of Progression = ((2*Sum of First N Terms of Progression)/(First Term of Progression+Nth Term of Progression)). Here is an example- 50.79365 = ((2*500)/(3+60)).

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

With Sum of First N Terms of Progression (S_n), First Term of Progression (a) & Nth Term of Progression (T_n) we can find Number of Terms of Arithmetic Progression given Sum of First N Terms using the formula - Index N of Progression = ((2*Sum of First N Terms of Progression)/(First Term of Progression+Nth Term of Progression)).

What are the other ways to Calculate Index N of Progression?

Here are the different ways to Calculate Index N of Progression-

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

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

​GoNumber of Terms of Arithmetic Progression Formula

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

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

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

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Other Formulas to find Index N of Progression

Other formulas in Number of Terms in Arithmetic Progression category

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

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

Variable Name

GoNumber of Terms of Arithmetic Progression Formula