formula.expertYour record

Geometric Series Sum

Sn=a1(1−rn)1−rS_n = \frac{a_1 (1 - r^{n})}{1 - r}

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

sig figs

Worked example: 3 + 6 + ... + 384 (8 terms) → S = 765. 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 Series Sum fits

In this toolkit

See also

Arithmetic Series Sum: Both use series sum and first term.Infinite Geometric Series: Both use series sum and first term.Geometric Sequence nth Term: Both use first term and Common ratio.Arithmetic Sequence nth Term: Both use first term.
Here the solver did the work. Could you?

Geometric series →

Grade 11Grade 11 Math: Functions & Applications

Test your skills in the Exam Room: new numbers every attempt. Free lessons for students, no sign-up, just pure learning.

See your Report Card
Learning zone

Geometric Series Sum explained

a1rSnn

Adding the first n terms of a geometric sequence collapses to a single fraction: a₁(1 − rⁿ)/(1 − r). The legendary chessboard reward (1 grain of wheat on the first square, doubling each square) sums to (2⁶⁴ − 1) ≈ 1.8 × 10¹⁹ grains over 64 squares, more wheat than the world has ever grown.

Shrinking ratios are just as practical: saving $100 in month one but only 80% as much each following month accumulates S = 100(1 − 0.8¹²)/(1 − 0.8) ≈ $465.64 over a year, already close to the $500 ceiling the infinite series would give.

Geometric Series Sum formula

Sn=a1(1−rn)1−rS_n = \frac{a_1 (1 - r^{n})}{1 - r}
Where
  • SnS_n= Sum of the first n terms
  • a1a_1= First term
  • rr= Common ratio
  • nn= Number of terms
In this toolkit

Arithmetic and geometric sequences

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

Revised 1 November 2026
Cite this page

formula.expert. (2026, November 1). Geometric Series Sum Formula & Calculator. https://formula.expert/solvers/geometric-series-sum

formula.experthttps://formula.expert/solvers/geometric-series-sum