Geometric Sequence Calculator
Enter the first term and the common ratio of a geometric sequence to find any term and the cumulative sum up to that term.
Geometric Sequence Calculator
Finds the nth term and the sum of the first n terms of a geometric sequence.
A geometric sequence multiplies by the same ratio at every step, and this calculator uses aₙ = a₁ × r^(n-1) for any term and the standard geometric series formula for the running sum. It automatically switches to a simpler sum formula when the ratio equals exactly 1, since the usual formula would otherwise divide by zero. Geometric sequences show up in compound growth, population models, and doubling/halving problems, making this a quick way to check such patterns without spreadsheet formulas.
Example
- With the default values shown above, this calculator returns: nth Term ≈ 486; Sum of First n Terms ≈ 728.
Frequently Asked Questions
What is a geometric sequence?
A sequence where each term is found by multiplying the previous term by a fixed ratio, e.g. 2, 6, 18, 54… (ratio 3).
What happens when the common ratio is 1?
When r = 1 every term equals the first term, so the sum is simply the first term multiplied by the number of terms — the calculator switches to that formula automatically to avoid dividing by zero.
Sources
- Standard formula, publicly documented method