Geometric Sequence Calculator
Find the nth term and sum of a geometric sequence. Calculate any term or partial sum given the first term and common ratio.
Enter the first term, common ratio, and term number.
Geometric Sequence Formulas
nth term: an = a₁ × r(n−1)
Sum of first n terms: Sn = a₁ × (1 − rn) / (1 − r) (r ≠ 1)
Infinite sum (|r| < 1): S∞ = a₁ / (1 − r)
Sum of first n terms: Sn = a₁ × (1 − rn) / (1 − r) (r ≠ 1)
Infinite sum (|r| < 1): S∞ = a₁ / (1 − r)
A geometric sequence is a sequence where each term is found by multiplying the previous term by a fixed number called the common ratio (r).
Example: a₁ = 3, r = 2, find a₅ and S₅
a₅ = 3 × 24 = 3 × 16 = 48
S₅ = 3 × (1 − 2⁵) / (1 − 2) = 3 × (−31) / (−1) = 93
Sequence: 3, 6, 12, 24, 48
a₅ = 3 × 24 = 3 × 16 = 48
S₅ = 3 × (1 − 2⁵) / (1 − 2) = 3 × (−31) / (−1) = 93
Sequence: 3, 6, 12, 24, 48
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Last updated: 2026-08-08