Geometric Sequence Calculator
Compute the nth term and sum of a geometric sequence.
Amortization schedule
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Showing first 12 of months.
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Introduction
Geometric Sequence Calculator — Compute the nth term and sum of a geometric sequence. Enter First term, Common ratio, n to get an instant, accurate result.
Formula
nth term = a₁ × rⁿ⁻¹. Sum of first n terms = a₁(1 − rⁿ)/(1 − r), where a₁ is the first term and r is the common ratio (sum = a₁ × n if r = 1).
Step-by-step
- Enter the First term.
- Enter the Common ratio.
- Enter the n.
- Click Calculate to see your result instantly.
Real-world example
Example: With First term = 2, Common ratio = 3, n = 6, the Geometric Sequence Calculator gives Nth Term: 486, Sum: 728.
Frequently Asked Questions
What happens if the ratio is 1?
Every term equals a₁, so the sum is simply a₁ multiplied by the number of terms.
Can the ratio be negative or a fraction?
Yes — a negative ratio alternates the sign of each term, and a fractional ratio (between −1 and 1) makes the sequence shrink toward zero.
What inputs does the Geometric Sequence Calculator need?
You'll need to provide: First term, Common ratio, n. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Geometric Sequence Calculator?
The Geometric Sequence Calculator applies the formula exactly as calculated — nth term = a₁ × rⁿ⁻¹. Sum of first n terms = a₁(1 − rⁿ)/(1 − r), where a₁ is the first term and r is the common ratio (sum = a₁ × n if r = 1). — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Geometric Sequence Calculator free to use?
Yes, the Geometric Sequence Calculator is completely free, requires no signup, and runs instantly in your browser.
About the Geometric Sequence Calculator
The Geometric Sequence Calculator uses a real, verifiable formula — nth term = a₁ × rⁿ⁻¹. Sum of first n terms = a₁(1 − rⁿ)/(1 − r), where a₁ is the first term and r is the common ratio (sum = a₁ × n if r = 1). — so results are accurate every time, not an approximation.