How to use the geometric sequence calculator
Find the nth term and sum of a geometric sequence. Enter first term, common ratio, number of terms in the fields above; the nth term, sum of n terms, infinite sum are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- a1 — First term
- r — Common ratio
- n — Number of terms
Worked example
With first term = 2, common ratio = 1.5, number of terms = 10, the calculator gives nth term ≈ 76.88672; sum of n terms ≈ 226.6602; infinite sum ≈ Diverges (|r| is 1 or more).
Frequently asked questions
What is the formula for the geometric sequence calculation?
nth term = a1 × r^(n-1). Sum of n terms = r===1?a1 × n:a1 × (1-r^n) / (1-r). Infinite sum = abs(r)<1?a1 / (1-r):"Diverges (|r| is 1 or more)". Here a1 is first term, r is common ratio, n is number of terms.
What inputs do I need for the geometric sequence calculator?
You need first term, common ratio, number of terms. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.