Geometric Sequence nth Term
Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!
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A geometric sequence multiplies by the same ratio r every step, so the nth term is the first term times r raised to (n − 1). Cell division is the classic case: starting from 1 cell that doubles each generation (r = 2), generation 11 has 1 × 2¹⁰ = 1024 cells. Ratios below 1 shrink instead — a ball rebounding to 60% of each bounce height that starts at 2 m reaches 2 × 0.6⁴ ≈ 0.26 m on the fifth bounce.
Solving for r extracts the per-step multiplier from two snapshots, and solving for n (with logarithms) answers "which step reaches this value?" This calculator keeps r positive so fractional positions stay real.
Geometric Sequence nth Term
Where
- = nth term
- = First term
- = Common ratio
- = Term number
Missing one of these? Work it out first, then come back
- nth term — Arithmetic Sequence nth Term, Arithmetic Series Sum
- First term — Arithmetic Sequence nth Term, Arithmetic Series Sum
- Common ratio — Infinite Geometric Series, Arithmetic Sequence nth Term
- Term number — Arithmetic Sequence nth Term, Arithmetic Series Sum