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Geometric Sequence Calculator
Find any term in a geometric sequence, plus the sum of all terms up to that point, from the first term and common ratio.
What a geometric sequence is
A geometric sequence is a list of numbers where each term is found by multiplying the previous term by a fixed value, called the common ratio. For example, 2, 6, 18, 54 is geometric with a common ratio of 3.
The formula used
The nth term of a geometric sequence is found with a_n = a1 × r^(n-1), where a1 is the first term and r is the common ratio. The sum of the first n terms is found with S_n = a1 × (1 – r^n) / (1 – r) when r is not equal to 1, or simply a1 × n when r equals 1.
This tool is intended for general math learning and educational purposes.
Last reviewed August 2026