How to use the Number Sequence Calculator
This tool works with arithmetic and geometric sequences, giving the nth term and the sum.
Open the Number Sequence Calculator →
What you need to enter
- Type
- First term
- Common difference / ratio
- Term number n
The formula
Arithmetic: aₙ = a₁ + (n − 1)d, sum = n(a₁ + aₙ) ÷ 2. Geometric: aₙ = a₁ × r^(n − 1), sum = a₁(1 − rⁿ) ÷ (1 − r).
Worked example
Using the default values in the calculator:
- Type: Arithmetic
- First term: 2
- Common difference / ratio: 3
- Term number n: 10
| n-th term | 29 |
| Sum of first n terms | 155 |
| First terms | 2, 5, 8, 11, 14, 17, 20, 23, 26, 29 |
Tips for better results
- Check whether the difference or ratio is constant.
- Test with small n first.
Common mistakes to avoid
- Using the wrong type.
- Off-by-one errors in n.