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Sum of First N Terms of Geometric 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{a \cdot (r^{n} - 1)}{r - 1}

S_n - Sum of First N Terms of Progression?a - First Term of Progression?r - Common Ratio of Progression?n - Index N of Progression?

Sum of First N Terms of Geometric Progression Example

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

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

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

189 = \frac{3 \cdot (2^{6} - 1)}{2 - 1}

189 = \frac{3 \cdot (2^{6} - 1)}{2 - 1}

189 = \frac{3 \cdot (2^{6} - 1)}{2 - 1}

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Sum of First N Terms of Geometric Progression Solution

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

FIRST Step Consider the formula

S n = \frac{a \cdot (r^{n} - 1)}{r - 1}

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

LAST Step Evaluate

∴

S n = 189

Sum of First N Terms of Geometric 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

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 Ratio of Progression

The Common Ratio of Progression is the ratio of any term to its preceding term of the Progression.

Symbol: r

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Common Ratio 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

Other formulas in Sum of Terms of Geometric Progression category

Go Sum of Infinite Geometric Progression

S ∞ = \frac{a}{1 - r ∞}

Go Common Ratio of Geometric Progression

r = \frac{T n}{T n-1}

Go Nth Term of Geometric Progression

T n = a \cdot (r^{n - 1})

Go Sum of Last N Terms of Geometric Progression

S n(End) = \frac{l \cdot ({(\frac{1}{r})}^{n} - 1)}{(\frac{1}{r}) - 1}

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

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

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

FAQs on Sum of First N Terms of Geometric Progression

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

The formula of Sum of First N Terms of Geometric Progression is expressed as Sum of First N Terms of Progression = (First Term of Progression*(Common Ratio of Progression^Index N of Progression-1))/(Common Ratio of Progression-1). Here is an example- 189 = (3*(2^6-1))/(2-1).

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

With First Term of Progression (a), Common Ratio of Progression (r) & Index N of Progression (n) we can find Sum of First N Terms of Geometric Progression using the formula - Sum of First N Terms of Progression = (First Term of Progression*(Common Ratio of Progression^Index N of Progression-1))/(Common Ratio of Progression-1).

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Sum of First N Terms of Geometric Progression Formula

Sum of First N Terms of Geometric Progression Example

Sum of First N Terms of Geometric Progression Solution

Sum of First N Terms of Geometric Progression Formula Elements

Other formulas in Sum of Terms of Geometric Progression category

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

FAQs on Sum of First N Terms of Geometric Progression

Variable Name