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Sum of First N Terms of Arithmetic Progression given NthTerm Formula

GoSum 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 (a + T n)

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

Sum of First N Terms of Arithmetic Progression given NthTerm Example

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

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

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

189 = (\frac{6}{2}) \cdot (3 + 60)

189 = (\frac{6}{2}) \cdot (3 + 60)

189 = (\frac{6}{2}) \cdot (3 + 60)

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Sum of First N Terms of Arithmetic Progression given NthTerm Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

S n = (\frac{6}{2}) \cdot (3 + 60)

Next Step Prepare to Evaluate

∴

S n = (\frac{6}{2}) \cdot (3 + 60)

LAST Step Evaluate

∴

S n = 189

Sum of First N Terms of Arithmetic Progression given NthTerm 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

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

Other Formulas to find Sum of First N Terms of Progression

Go Sum of First N Terms of Arithmetic Progression

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

Other formulas in Sum of Terms of Arithmetic Progression category

Go Sum of Total Terms of Arithmetic Progression

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

Go Sum of Total Terms of Arithmetic Progression given Last Term

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

Go Sum of Last N Terms of Arithmetic Progression given Last Term

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

Go Sum of Last N Terms of Arithmetic Progression

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

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

Sum of First N Terms of Arithmetic Progression given NthTerm evaluator uses Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term of Progression) to evaluate the Sum of First N Terms of Progression, The Sum of First N Terms of Arithmetic Progression given NthTerm formula is defined as the summation of the terms starting from the first to the nth term of given Arithmetic Progression, and is calculated using the nth term of the 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 given NthTerm using this online evaluator? To use this online evaluator for Sum of First N Terms of Arithmetic Progression given NthTerm, enter Index N of Progression (n), First Term of Progression (a) & Nth Term of Progression (T_n) and hit the calculate button.

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

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

The formula of Sum of First N Terms of Arithmetic Progression given NthTerm is expressed as Sum of First N Terms of Progression = (Index N of Progression/2)*(First Term of Progression+Nth Term of Progression). Here is an example- 189 = (6/2)*(3+60).

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

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

What are the other ways to Calculate Sum of First N Terms of Progression?

Here are the different ways to Calculate Sum of First N Terms of Progression-

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 given NthTerm Formula

​GoSum of First N Terms of Arithmetic Progression Formula

Sum of First N Terms of Arithmetic Progression given NthTerm Example

Sum of First N Terms of Arithmetic Progression given NthTerm Solution

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

Other Formulas to find Sum of First N Terms of Progression

Other formulas in Sum of Terms of Arithmetic Progression category

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

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

Variable Name

GoSum of First N Terms of Arithmetic Progression Formula