Geometric Sequence Calculator
aₙ = a₁ × r^(n−1). Find any term of a geometric sequence.
Result
a10
39,366.000000
Sum of first 10 terms: 59,048.0000.
- a₁2
- r3
- n10
- aₙ39,366.000000
- Sum 1..n59,048.0000
- First 5 terms2.0000, 6.0000, 18.0000, 54.0000, 162.0000
Step-by-step
- aₙ = a₁ × r^(n−1) = 2 × 3^9 = 39,366.0000.
- Sₙ = a₁(1 − r^n) / (1 − r) = 59,048.0000.
How to use this calculator
- Enter a₁, ratio r, and n.
About this calculator
Geometric sequence: each term is the previous × constant ratio r. Formula aₙ = a₁ × r^(n−1). Sum: Sₙ = a₁(1 − rⁿ)/(1 − r) for r ≠ 1. Examples: doubling (r=2), halving (r=½), compound interest (r = 1+rate), bouncing-ball heights (r<1), nuclear chain reactions. Infinite sum converges if |r| < 1: S∞ = a₁/(1−r).
Frequently asked
All terms equal a₁; sum = n × a₁. Standard formula has 0/0; this calc handles separately.
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