Formula and method
aₙ = a₁ + (n − 1)d. The sum is Sₙ = n(a₁ + aₙ)/2, with term numbering starting at one.
Worked example
Starting at 2 with difference 3, the tenth term is 29 and the first ten terms sum to 155.
Arithmetic Sequence Calculator
Find an arithmetic sequence’s nth term, finite sum and first terms from the initial value and common difference.
Printed from Calxy · https://www.calxy.net/math/arithmetic-sequence-calculator
Term 1029.0000
-1000000000 – 1000000000
-1000000000 – 1000000000
terms
1 – 10000
Term 10
29.0000
- Sum of first 10 terms155.0000
| Index | Term |
|---|---|
| 1 | 2 |
| 2 | 5 |
| 3 | 8 |
| 4 | 11 |
| 5 | 14 |
| 6 | 17 |
| 7 | 20 |
| 8 | 23 |
| 9 | 26 |
| 10 | 29 |
Term indices start at 1. Very large geometric powers can exceed floating-point range; reduce the term count or ratio if the calculator reports an overflow.
How this was calculated
aₙ = a₁ + (n − 1)d.
Sₙ = n(a₁ + aₙ)/2.
Frequently asked questions
Can the difference be negative?
Yes. A negative difference creates a decreasing sequence. Term counts must remain positive whole numbers.
Last updated . Results are estimates for informational purposes only.