Geometric Sequence Calculator
nth term and sum of a geometric series.
Enter your values
Enter the first term you are working with.
Enter the common ratio you are working with.
Enter the term number you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Term 10
- 1536
- Sum of first n terms
- 3069
- Infinite sum
- Diverges
- Common ratio
- 2
- First terms
- 3, 6, 12, 24, 48, 96, 192, 384
Quick answer
Each geometric term multiplies the previous by a constant ratio r, so aₙ = a₁r^(n−1).
aₙ = a₁r^(n−1), Sₙ = a₁(1−rⁿ)/(1−r)
At a glance
| What it does | nth term and sum of a geometric series. |
|---|---|
| Category | Math |
| Inputs needed | First term, Common ratio, Term number |
| Main output | Term 10 |
| Formula | aₙ = a₁r^(n−1), Sₙ = a₁(1−rⁿ)/(1−r) |
| Cost | Free — no sign-up, no download |
How to use the Geometric Sequence Calculator
- 1Enter the first term.
- 2Enter the common ratio between terms.
- 3Enter the term number you need.
Inputs explained
- First term
- Enter the first term you are working with.
- Common ratio
- Enter the common ratio you are working with.
- Term number
- Enter the term number you are working with.
Worked example
Using the values the calculator loads with:
Inputs
- First term3
- Common ratio2
- Term number10
Results
- Term 101536
- Sum of first n terms3069
- Infinite sumDiverges
- Common ratio2
- First terms3, 6, 12, 24, 48, 96, 192, 384
Frequently asked questions
When does an infinite series converge?
Only when |r| < 1.
Can the ratio be negative?
Yes — the terms then alternate in sign.
What do I need to enter into the Geometric Sequence Calculator?
Just 3 values: first term, common ratio, term number. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Geometric Sequence Calculator work out the answer?
Each geometric term multiplies the previous by a constant ratio r, so aₙ = a₁r^(n−1). It applies the formula aₙ = a₁r^(n−1), Sₙ = a₁(1−rⁿ)/(1−r) and shows the working so you can check each step by hand.
Is the Geometric Sequence Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.