Number Sequence Calculator
Find the n-th term and sum of the first n terms of arithmetic or geometric sequences.
Input Data
Results
21
120
arithmetic sequence, n=10
At a glance:Arithmetic: aₙ = a₁ + (n−1)d, Sₙ = n/2·(2a₁ + (n−1)d). Geometric: aₙ = a₁·r^(n−1), Sₙ = a₁·(1−rⁿ)/(1−r) for r≠1; at r=1, Sₙ = a₁·n.
Formula
Arithmetic: aₙ = a₁+(n−1)d; Sₙ = n(a₁+aₙ)/2.
Geometric: aₙ = a₁r^(n−1); Sₙ = a₁(1−rⁿ)/(1−r).
How to Use
- Pick a type.
- Enter a₁, d or r, and n.
- Read aₙ and Sₙ.
FAQ
Geometric r=1?
All terms are equal, so the sum is a₁·n.
Can n be large?
Yes; geometric terms and sums can grow huge, computed at high precision.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only.