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Geometric Sequence nth Term

an=a1 r n−1a_n = a_1 \, r^{\,n-1}

Units aren’t used in this calculation: every value is a plain number.

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Worked example: 3, 6, 12, ... 8th term → 384. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value.

Where Geometric Sequence nth Term fits

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See also

Arithmetic Sequence nth Term: Both use nth term and first term.Geometric Series Sum: Both use first term and Common ratio.Infinite Geometric Series: Both use first term and Common ratio.Arithmetic Series Sum: Both use first term.
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Geometric Sequence nth Term explained

ra1ann

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 formula

an=a1 r n−1a_n = a_1 \, r^{\,n-1}
Where
  • ana_n= nth term
  • a1a_1= First term
  • rr= Common ratio
  • nn= Term number
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Arithmetic and geometric sequences

5 formulasThe nth term and the sum for both arithmetic and geometric progressions, including the infinite sum that converges.

Revised 31 October 2026
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formula.expert. (2026, October 31). Geometric Sequence nth Term Formula & Calculator. https://formula.expert/solvers/geometric-nth-term

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