Sequence Calculator
Find the nth term and sum of arithmetic or geometric sequences. Enter the first term, common difference or ratio, and the number of terms.
Enter values to find the nth term and sum.
Arithmetic Sequence Formula
nth term: an = a₁ + (n − 1) × d
Sum: Sn = n/2 × (2a₁ + (n − 1) × d)
Sum: Sn = n/2 × (2a₁ + (n − 1) × d)
Geometric Sequence Formula
nth term: an = a₁ × r(n−1)
Sum: Sn = a₁ × (1 − rn) / (1 − r) when r ≠ 1
Sum: Sn = a₁ × (1 − rn) / (1 − r) when r ≠ 1
Example (Arithmetic): a₁ = 3, d = 5, n = 7
7th term = 3 + (7−1) × 5 = 3 + 30 = 33
Sum = 7/2 × (6 + 30) = 3.5 × 36 = 126
7th term = 3 + (7−1) × 5 = 3 + 30 = 33
Sum = 7/2 × (6 + 30) = 3.5 × 36 = 126
FAQ
What is the difference between arithmetic and geometric sequences?
In an arithmetic sequence, each term differs by a constant amount (common difference). In a geometric sequence, each term is multiplied by a constant factor (common ratio).
Can a geometric sequence have a negative ratio?
Yes. A negative common ratio produces terms that alternate between positive and negative values.
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Last updated: 2026-08-08