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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.

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.

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