# Geometric Sequences

In this worksheet, students find the missing term in geometric sequences.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Use Geometric Sequences

Difficulty level:

### QUESTION 1 of 10

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 ...

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

Work out the missing term in this geometric sequence:

1, 2, 4, ?, 16, 32...

Work out the missing term in this geometric sequence:

2, 4, ?, 16, 32, 64 ...

Work out the missing term in this geometric sequence:

5, 10, 20, ?, 80, 160...

Work out the missing term in this geometric sequence:

3, 9, 27, ?, 243, 729...

Work out the missing term in this geometric sequence:

2, 6, 18, ?, 162, 486 ...

Work out the missing term in this geometric sequence:

1200, 600, 300, ?, 75...

Work out the missing term in this geometric sequence:

1215, 405, 135, ?, 15, 5...

Work out the missing term in this geometric sequence:

1, -2, 4, ?, 16, -32...

Work out the missing term in this geometric sequence:

625, 125, 25, ?, 1, 0.2...

Work out the missing term in this geometric sequence:

0.001, 0.01, ?, 1, 10...

• Question 1

Work out the missing term in this geometric sequence:

1, 2, 4, ?, 16, 32...

8
EDDIE SAYS
The common ratio is 2. This means we have to multiply 4 by 2 to get our missing number.
• Question 2

Work out the missing term in this geometric sequence:

2, 4, ?, 16, 32, 64 ...

8
EDDIE SAYS
The common ratio is 2. This means we have to multiply 4 by 2 to get our missing number.
• Question 3

Work out the missing term in this geometric sequence:

5, 10, 20, ?, 80, 160...

40
EDDIE SAYS
The common ratio is 2. This means we have to multiply 20 by 2 to get our missing number.
• Question 4

Work out the missing term in this geometric sequence:

3, 9, 27, ?, 243, 729...

81
EDDIE SAYS
The common ratio is 3. This means we have to multiply 27 by 3 to get our missing number.
• Question 5

Work out the missing term in this geometric sequence:

2, 6, 18, ?, 162, 486 ...

54
EDDIE SAYS
The common ratio is 3. This means we have to multiply 18 by 3 to get our missing number.
• Question 6

Work out the missing term in this geometric sequence:

1200, 600, 300, ?, 75...

150
EDDIE SAYS
The common ratio is ½. This means we have to multiply 300 by ½ to get our missing number. This is exactly the same as dividing by 3
• Question 7

Work out the missing term in this geometric sequence:

1215, 405, 135, ?, 15, 5...

45
EDDIE SAYS
The common ratio is 1/3. This means we have to multiply 135 by 1/3 to get our missing number. This is exactly the same as dividing by 3
• Question 8

Work out the missing term in this geometric sequence:

1, -2, 4, ?, 16, -32...

-8
EDDIE SAYS
The common ratio is -2. This means we have to multiply 4 by -2 to get our missing number.
• Question 9

Work out the missing term in this geometric sequence:

625, 125, 25, ?, 1, 0.2...

5
EDDIE SAYS
The common ratio is 1/5. This means we have to multiply 25 by 1/5 to get our missing number. This is exactly the same as dividing by 5
• Question 10

Work out the missing term in this geometric sequence:

0.001, 0.01, ?, 1, 10...

0.1
EDDIE SAYS
The common ratio is 10. This means we have to multiply 0.01 by 10 to get our missing number.
---- OR ----

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