Geometric Sequence Calculator
Find the nth term, sum, and properties of a geometric sequence given the first term, common ratio, and number of terms.
Nth Term
486.0000
Sum Infinite0.000000
Geometric Sequence
nth Term
aₙ = a₁ × r^(n-1)
Sum of n Terms
Sₙ = a₁ × (1 - r^n) / (1 - r) (when r ≠ 1)
Infinite Sum (converges only when r
S∞ = a₁ / (1 - r)
A geometric sequence has a constant ratio between consecutive terms.
Example Calculation
Geometric sequence: first term = 2, common ratio = 3, 6 terms.
- 01a₆ = 2 × 3⁵ = 2 × 243 = 486
- 02Sum = 2 × (1 - 3⁶) / (1 - 3) = 2 × (1 - 729) / (-2) = 728
- 03Sequence: 2, 6, 18, 54, 162, 486
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