Sequence calculator

Enter a sequence to detect its pattern, find the nth term formula, or compute the nth term of an arithmetic/geometric sequence.

Mode

Sequence

Arithmetic: Each term differs by a constant (common difference d). Formula: aₙ = a₁ + (n−1)d. Example: 2, 5, 8, 11, 14 (d = 3).

Geometric: Each term is multiplied by a constant (common ratio r). Formula: aₙ = a₁ × r^(n−1). Example: 3, 6, 12, 24, 48 (r = 2).

Fibonacci-like: Each term is the sum of the two previous terms. Example: 1, 1, 2, 3, 5, 8, 13.

Sum of first n terms: S = n/2 × (first term + last term) = n/2 × (2a₁ + (n−1)d).

Sum of 2+5+8+...+59 (20 terms): S = 20/2 × (2+59) = 610.

Finite sum: S = a₁(1 − rⁿ)/(1 − r) for r ≠ 1.

Infinite sum (|r| < 1): S = a₁/(1 − r). Example: 1 + 1/2 + 1/4 + ... = 2.