Geometric Sequence Calculator
First term (a₁)
Common ratio (r)
Number of terms (≤20)
A geometric sequence has each term as a constant multiple (common ratio r) of the previous term. Geometric sequences model exponential growth, compound interest, and population dynamics.
- 1aₙ = a₁ × rⁿ⁻¹
- 2Sum of n terms: Sₙ = a₁(1−rⁿ)/(1−r)
- 3Sum to infinity (|r|<1): S∞ = a₁/(1−r)
- 4Ratio r = aₙ/aₙ₋₁
a₁ = 2, r = 3, 5 terms=2, 6, 18, 54, 162 — Sum = 242
a₁ = 1, r = 0.5, ∞ terms=Sum to infinity = 1/(1−0.5) = 2
| r | S₅ | S₁₀ | S∞ |
|---|---|---|---|
| 0.5 | 1.9375 | 1.999 | 2 |
| 0.9 | 4.095 | 6.513 | 10 |
| 2 | 31 | 1023 | ∞ |
| 3 | 121 | 29524 | ∞ |
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