Geometric Series Sum Calculator
Find the sum and last term of a geometric series from the first term, ratio, and count.
Last updated:
Input
Enter the first term, common ratio, and number of terms to compute the sum and last term of the geometric series.
The sequence runs a, ar, ar², … and the sum is S=a(1−rⁿ)/(1−r), or S=an when r=1.
Result
Sum S
242
Last term (nth term)
162
First term
2
Terms
5
Leading terms
2
,
6
,
18
,
54
,
162
The sum is computed with the formula S=a(1−rⁿ)/(1−r).
How it works
- 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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