Geometric Sequence Calculator
Every sequence problem starts with three values: the first term, the common ratio and the term number. Enter a, r and n here to get the nth term, the full list of terms and their sum — with each step shown.
How to use
- Enter the first term (a) of your sequence.
- Enter the common ratio (r) — the number each term is multiplied by.
- Enter the term number (n) you want to find.
- Read the nth term, the full list of terms and the sum, with each calculation step shown.
Note: If r = 1, all terms are equal and sum = n x a.
Tips
- If the ratio is between 0 and 1, the terms shrink toward zero — check that the result looks sensible.
- For ratio r = 1, every term equals the first term, and the sum is simply n times a.
- Negative ratios alternate the sign of each term — this is correct, not an error.
- The sum formula here covers only the finite first n terms, not infinite series.
Frequently Asked Questions (FAQ)
What does the Geometric Sequence Calculator do?
Enter the first term (a), common ratio (r) and term number (n) to get the nth term, the first n terms and the sum of terms.
Which formula is used for the nth term?
nth term = a x r^(n-1), shown with each step so you can follow the calculation.
How is the sum of the terms calculated?
The tool adds up the first n terms for you and shows each step, so you can see exactly how the total is built.
What happens if r = 1?
All terms are equal and the sum = n x a.