Find the Missing Terms in Geometric Sequences

A geometric sequence or progression is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number, called the common ratio.

This means that dividing consecutive terms gives the same number.

5, 50, 500, 5000, 50000 ...

is a geometric sequence in which the common ratio is 10.

1500, 150, 15, 1.5, 0.15 ...

is a geometric sequence in which the common ratio is 1/10.

Example

Work out the missing term in this geometric sequence:

7, 14, 28, ?, 112, 224 ...

Answer

Look at the first few terms in pairs to work out the common ratio.

14 ÷  7 = 2

28 ÷ 14 = 2

224 ÷ 112 = 2

The common ratio is 2, so the missing term is

28 x 2 = 56

Let's practise this in the following questions.