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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

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

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