Geometric Sequence Table: nth term by First term (a)
Reference table of nth term for Geometric Sequence across a range of first term (a) values — exact, engine-computed figures you can read off at a glance.
Geometric Sequence Calculator
Verified formula Updated Jun 2026 Private — runs on your device
Verified formula
Private
nth term
162.0000
- Sum of first n terms
- 242.0000
For general information only — not financial, tax, legal or medical advice. Verify before you rely on it.
How to use the Geometric Sequence Calculator
The Geometric Sequence Calculator works out your nth term, along with 1 related figure in an instant. Enter first term (a), common ratio (r) and term number (n) and the result updates as you type — it is free, needs no sign-up, and runs entirely in your browser so your figures stay private.
- Enter the first term (a).
- Enter the common ratio (r).
- Enter the term number (n).
- Read off your nth term, together with sum of first n terms — the calculator updates automatically, with no button to press.
Formula
The Geometric Sequence Calculator uses the formula:
nth term = First term (a) × (Common ratio (r))^(Term number (n) - 1)
Worked example
For example, with first term (a) of 2, common ratio (r) of 3 and term number (n) of 5, the nth term is 162.0000.
| First term (a) | 2 |
|---|---|
| Common ratio (r) | 3 |
| Term number (n) | 5 |
| nth term | 162.0000 |
|---|---|
| Sum of first n terms | 242.0000 |
Results are estimates for educational use, not professional advice.
Key terms explained
- Ratio
- A comparison of two quantities showing how many times one contains the other.
Frequently asked questions
It is a list of numbers where each term is multiplied by a fixed ratio. Starting at 2 with a ratio of 3 gives 2, 6, 18, 54, …
Use a × r^(n − 1). The 5th term of the sequence starting at 2 with ratio 3 is 2 × 3⁴ = 162.
The sum of the first n terms is a × (rⁿ − 1) ÷ (r − 1). For the first 5 terms above, the sum is 242.
The terms shrink toward zero. Such sequences have a finite sum even when continued forever, which is an infinite geometric series.
Enter the first term (a). Enter the common ratio (r). Enter the term number (n). Read off your nth term, together with sum of first n terms — the calculator updates automatically, with no button to press.
Related guides
How to Calculate Geometric Sequence: Formula, Steps & Examples
Learn how to calculate Geometric Sequence — the formula explained step by step, with worked examples and a free calculator to check your answer.