Infinite Geometric Series

Free interactive math game: Infinite Geometric Series — S = a₁/(1−q). 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. Infinite geometric series: a₁ = 6, q = 1/4 S = ?
  2. Infinite geometric series: a₁ = 3, q = 1/4 S = ?
  3. Infinite geometric series: a₁ = 12, q = 1/3 S = ?
  4. Infinite geometric series: a₁ = 24, q = 1/5 S = ?

About this exercise

The total of a geometric series that never ends.

How to solve it

When the ratio lies between -1 and 1, divide the first term by one minus the ratio.

Worked example

With a first term of 1 and a ratio of a half, the sum is 1 : 0.5 = 2.

Common mistake

Applying it when the ratio is 1 or more. Those series grow without limit and have no sum.