Arithmetic Sequence
An arithmetic sequence increases by a fixed common difference d. This calculator finds the nth term with aₙ = a₁ + (n − 1)d and the sum of the first n terms with Sₙ = n/2·(a₁ + aₙ).
Worked examples
Frequently asked questions
What is the nth term formula?
The nth term is aₙ = a₁ + (n − 1)d, where a₁ is the first term and d the common difference.
How is the sum calculated?
The partial sum is Sₙ = n/2·(a₁ + aₙ), the number of terms times the average of the first and last term.
Can the common difference be negative?
Yes. A negative common difference produces a decreasing sequence.