Geometric Series Sum Calculator

Find the sum and last term of a geometric series from the first term, ratio, and count.

Input

Enter the first term, common ratio, and number of terms to compute the sum and last term of the geometric series.

First term a

Common ratio r

Number of terms n

The sequence runs a, ar, ar², … and the sum is S=a(1−rⁿ)/(1−r), or S=an when r=1.

Sum S

242

Last term (nth term)

162

First term

Terms

Leading terms

162

The sum is computed with the formula S=a(1−rⁿ)/(1−r).

A geometric series is a sequence where each term is the previous term multiplied by a fixed number called the common ratio r. With first term a and n terms, the terms are a, ar, ar squared, up to a times r to the power n minus one.
The nth term, also called the last term, equals a times r to the power n minus one.
When the common ratio r is not equal to 1, the sum is S=a(1−rⁿ)/(1−r).
When the common ratio r equals 1, every term equals the first term a, so the sum is S=an, that is a multiplied by n.
Enter an integer of 1 or more for the number of terms n. The first term a and ratio r may be decimals or negative numbers.

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