Fraction Geometric Sequence

Free interactive math game: Fraction Geometric Sequence — 1, 1/2, 1/4, ?. 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. 1, 1/4, 1/16, 1/64, ? (Geometric sequence with q = 1/4)
  2. 1, 1/3, 1/9, 1/27, ? (Geometric sequence with q = 1/3)
  3. 1, 1/2, 1/4, 1/8, ? (Geometric sequence with q = 1/2)

About this exercise

Geometric sequences whose ratio is a fraction, so the terms shrink.

How to solve it

Multiply by the fractional ratio each time, which is the same as dividing by its reciprocal.

Worked example

In 16, 8, 4 the ratio is a half, so the next term is 2.

Common mistake

Expecting the terms to reach zero. They keep halving and get closer without ever arriving.