MihsabaHow to use
An arithmetic sequence changes by a constant amount from one term to the next. Enter the first term, common difference and term number to get the nth term, partial sum, average and an initial preview.
- Enter first term a₁.
- Enter common difference d, which may be negative or zero.
- Enter positive integer term number n.
- Review aₙ, Sₙ, the average and the first terms.
How it is calculated
aₙ=a₁+(n−1)d; Sₙ=n(a₁+aₙ)÷2
Example
With a₁=5, d=3 and n=10, a₁₀=32, the first-ten-term sum is 185 and their average is 18.5.
Important notes
Term numbering starts at 1. If d=0, every term is equal. Extremely large inputs can exceed the browser’s finite-number range.
Frequently asked questions
Difference vs ratio?
Arithmetic sequences add d each step; geometric sequences multiply by r.
Can d be negative?
Yes. The sequence then decreases by a constant amount.
How is the sum found?
Sₙ=n(a₁+aₙ)/2.
Is this calculator free?
Yes. It is free to use and requires no account.