Sum of Geometric

Free interactive math game: Sum of Geometric — Sₙ = a₁(qⁿ−1)/(q−1). Part of the Sequences category on MathKite.

Example problems

Taken from the generator that powers this exercise. A fresh set appears every time the page is opened, and the printable worksheet holds ten of them.

  1. Geometric sequence: a₁ = 4, q = 4 Find S₅ (sum of first 5 terms).
  2. Geometric sequence: a₁ = 5, q = 3 Find S₄ (sum of first 4 terms).
  3. Geometric sequence: a₁ = 3, q = 3 Find S₅ (sum of first 5 terms).
  4. Geometric sequence: a₁ = 4, q = (-2) Find S₃ (sum of first 3 terms).

About this exercise

The running total of a geometric sequence after n terms.

How to solve it

Raise the ratio to the power n, subtract 1, divide by the ratio minus 1, and multiply all of that by the first term.

Worked example

For a first term 4 and ratio 4, the total of four terms is 4 x (256 - 1) : (4 - 1) = 4 x 85 = 340.

Common mistake

Using the arithmetic sum formula. Geometric terms grow far too fast for averaging to work.