Find the n-th term and the sum of an arithmetic or geometric sequence.
What this calculator does
Enter the first term, the common difference or ratio, and a term number, and this calculator returns the n-th term and the sum of the first n terms.
It handles both arithmetic (add a constant) and geometric (multiply by a constant) sequences.
Getting your answer
- Choose arithmetic or geometric.
- Enter the first term and the difference or ratio.
- Enter n to get the term and sum.
How the number is calculated
arithmetic: aₙ = a₁ + (n−1)d
geometric: aₙ = a₁ × r^(n−1)
A worked example
Worked through, a term n of 10 produces a n-th term of 29. Underneath, Sum of first n comes out at 155 and Sequence at 2, 5, 8, 11, 14, 17, 20, 23…. Change any field and every figure updates as you type.
FAQ
What’s an arithmetic sequence?
One where each term differs from the last by a constant amount, like 2, 5, 8, 11 (difference 3).
What’s a geometric sequence?
One where each term is the previous times a constant ratio, like 2, 6, 18, 54 (ratio 3).
How do I sum a sequence?
Arithmetic sums use n/2 × (2a₁ + (n−1)d); geometric sums use a₁(rⁿ−1)/(r−1). The tool does both.