Calculating your nth term is straightforward once you know the Geometric Sequence formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Geometric Sequence Calculator.
What is Geometric Sequence?
The Geometric Sequence calculation tells you your nth term from a few simple inputs. The figure you are solving for here is the nth term.
The Geometric Sequence formula
The core formula is:
nth term = First term (a) × (Common ratio (r))^(Term number (n) - 1)Here is what each input means:
- First term (a) — a number. Example: 2.
- Common ratio (r) — a number. Example: 3.
- Term number (n) — a number. Example: 5.
How to calculate it step by step
- Write down the first term (a) (for example, 2).
- Write down the common ratio (r) (for example, 3).
- Write down the term number (n) (for example, 5).
- Apply the formula above to get your nth term.
- Double-check the result with the Geometric Sequence Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| First term (a) | 2 |
| Common ratio (r) | 3 |
| Term number (n) | 5 |
| nth term | 162.0000 |
| Sum of first n terms | 242.0000 |
With first term (a) of 2, common ratio (r) of 3 and term number (n) of 5, the nth term works out to 162.0000.
Example 2
With first term (a) of 4, common ratio (r) of 3 and term number (n) of 5, the nth term works out to 324.0000.
| Result | Value |
|---|---|
| nth term | 324.0000 |
| Sum of first n terms | 484.0000 |
Example 3
With first term (a) of 1, common ratio (r) of 3 and term number (n) of 5, the nth term works out to 81.0000.
| Result | Value |
|---|---|
| nth term | 81.0000 |
| Sum of first n terms | 121.0000 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Geometric Sequence Calculator does it instantly, for free, with the formula and a worked example built in.
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