Geometric Sequence Calculator
The nth term and the sum of a geometric sequence.
Result
nth term
162.00
Sum of n terms
242.00
How it works
aₙ = a₁ · r^(n−1), Sₙ = a₁ (rⁿ−1)/(r−1)
In a geometric sequence each term multiplies by a fixed ratio. Terms grow (or shrink) exponentially, and the sum has a neat closed form.
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Frequently asked questions
What is the common ratio?
The fixed factor multiplied between consecutive terms — for example 3 in 2, 6, 18, 54.
When does the sum converge?
For an infinite series it converges only when the ratio is between −1 and 1.
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