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Geometric Sequence Calculator

Compute the nth term and partial sum of a geometric sequence from the first term and common ratio, and list the terms.

Also known as geometric progression, gp calculator, nth term geometric.

Enter values

Results update as you type.

Result

a8

4,374

Sum of 8 terms
6,560
Sequence
2, 6, 18, 54, 162, 486, 1,458, 4,374
Step-by-stepShow
  1. aₙ = 2 × 3^7 = 4,374
  2. Sₙ = 2(1 − 3^8) / (1 − 3) = 6,560

About the Geometric Sequence Calculator

Compute the nth term and partial sum of a geometric sequence from the first term and common ratio, and list the terms.

Also known as: geometric progression, gp calculator, nth term geometric, exponential sequence.

How to use this calculator

  1. Enter first term (a₁), common ratio (r), number of terms (n).
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Open “Step-by-step” to see how the answer was worked out.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Geometric Sequence formula

aₙ = a₁·rⁿ⁻¹ · Sₙ = a₁(1 − rⁿ)/(1 − r)

Worked example

Using the values pre-filled in the calculator above:

  • First term (a₁) = 2
  • Common ratio (r) = 3
  • Number of terms (n) = 8

the calculator returns:

  • a8: 4,374
  • Sum of 8 terms: 6,560
  • Sequence: 2, 6, 18, 54, 162, 486, 1,458, 4,374

Working

  1. aₙ = 2 × 3^7 = 4,374
  2. Sₙ = 2(1 − 3^8) / (1 − 3) = 6,560