Sequence Calculator
Detect arithmetic or geometric sequences and calculate the nth term, sum, and first 10 terms.
nth Term (aₙ)
—
Sum (Sₙ)
—
First 10 Terms
What is Sequence Calculator?
A sequence calculator automatically detects whether your sequence is arithmetic (constant difference) or geometric (constant ratio), then calculates the nth term, partial sum, and lists the first 10 terms. It covers the two most common types of mathematical sequences used in algebra, finance, and science.
How to use
- 1 Enter the first term (a₁) of the sequence.
- 2 Enter either the common difference (d) for arithmetic or the common ratio (r) for geometric.
- 3 Enter n — the term number you want to find.
- 4 Select whether the sequence is arithmetic or geometric.
- 5 Results appear instantly.
Formula
Example calculation
Arithmetic: a₁=2, d=3, n=5 → a₅ = 2 + 4×3 = 14. S₅ = 5/2 × (4 + 12) = 40. Geometric: a₁=3, r=2, n=5 → a₅ = 3×2⁴ = 48. S₅ = 3×(1−32)/(1−2) = 93.
Frequently asked questions
What is an arithmetic sequence?
An arithmetic sequence has a constant difference between consecutive terms. For example: 2, 5, 8, 11 (d=3).
What is a geometric sequence?
A geometric sequence has a constant ratio between consecutive terms. For example: 3, 6, 12, 24 (r=2).
What happens when r=1 in a geometric sequence?
When r=1, every term is equal to a₁, so the sum is simply n × a₁.
Can d or r be negative?
Yes. A negative d creates a decreasing arithmetic sequence. A negative r creates an alternating geometric sequence (terms flip sign each step).
What is the sum formula for an infinite geometric series?
If |r| < 1, the infinite sum converges to S = a₁ / (1−r). This calculator handles finite sums only.