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Sum of First N Terms of Arithmetic Progression Formula

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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. Check FAQs

S n = (\frac{n}{2}) \cdot ((2 \cdot a) + ((n - 1) \cdot d))

S_n - Sum of First N Terms of Progression?n - Index N of Progression?a - First Term of Progression?d - Common Difference of Progression?

Sum of First N Terms of Arithmetic Progression Example

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

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

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

78 = (\frac{6}{2}) \cdot ((2 \cdot 3) + ((6 - 1) \cdot 4))

78 = (\frac{6}{2}) \cdot ((2 \cdot 3) + ((6 - 1) \cdot 4))

78 = (\frac{6}{2}) \cdot ((2 \cdot 3) + ((6 - 1) \cdot 4))

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Sum of First N Terms of Arithmetic Progression Solution

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

FIRST Step Consider the formula

S n = (\frac{n}{2}) \cdot ((2 \cdot a) + ((n - 1) \cdot d))

Next Step Substitute values of Variables

∴

S n = (\frac{6}{2}) \cdot ((2 \cdot 3) + ((6 - 1) \cdot 4))

Next Step Prepare to Evaluate

∴

S n = (\frac{6}{2}) \cdot ((2 \cdot 3) + ((6 - 1) \cdot 4))

LAST Step Evaluate

∴

S n = 78

Sum of First N Terms of Arithmetic Progression Formula Elements

Variables

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

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

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

Common Difference of Progression

The Common Difference of Progression is the difference between two consecutive terms of a Progression, which is always a constant.

Symbol: d

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Common Difference of Progression

Credits

Created by Nikita Salampuria

The National Institute of Engineering (NIE), Mysuru

Nikita Salampuria has created this Formula and 25+ more formulas!

Verified by Nayana Phulphagar

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

Nayana Phulphagar has verified this Formula and 1500+ more formulas!

Other formulas in Sum of Terms of Arithmetic Progression category

Go Common Difference of Arithmetic Progression

d = T n - T n-1

Go Nth Term of Arithmetic Progression

T n = a + (n - 1) \cdot d

Go Sum of Total Terms of Arithmetic Progression given Last Term

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

Go Common Difference of Arithmetic Progression given Last Term

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

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

Sum of First N Terms of Arithmetic Progression evaluator uses Sum of First N Terms of Progression = (Index N of Progression/2)*((2*First Term of Progression)+((Index N of Progression-1)*Common Difference of Progression)) to evaluate the Sum of First N Terms of Progression, The Sum of First N Terms of Arithmetic Progression formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Progression. Sum of First N Terms of Progression is denoted by S_n symbol.

How to evaluate Sum of First N Terms of Arithmetic Progression using this online evaluator? To use this online evaluator for Sum of First N Terms of Arithmetic Progression, enter Index N of Progression (n), First Term of Progression (a) & Common Difference of Progression (d) and hit the calculate button.

FAQs on Sum of First N Terms of Arithmetic Progression

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

The formula of Sum of First N Terms of Arithmetic Progression is expressed as Sum of First N Terms of Progression = (Index N of Progression/2)*((2*First Term of Progression)+((Index N of Progression-1)*Common Difference of Progression)). Here is an example- 78 = (6/2)*((2*3)+((6-1)*4)).

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

With Index N of Progression (n), First Term of Progression (a) & Common Difference of Progression (d) we can find Sum of First N Terms of Arithmetic Progression using the formula - Sum of First N Terms of Progression = (Index N of Progression/2)*((2*First Term of Progression)+((Index N of Progression-1)*Common Difference of Progression)).

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Sum of First N Terms of Arithmetic Progression Formula

Sum of First N Terms of Arithmetic Progression Example

Sum of First N Terms of Arithmetic Progression Solution

Sum of First N Terms of Arithmetic Progression Formula Elements

Credits

Other formulas in Sum of Terms of Arithmetic Progression category

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

FAQs on Sum of First N Terms of Arithmetic Progression

Variable Name