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Arithmetic Sequences

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

'Arithmetic Sequences' worksheet

Key stage:  KS 3

Curriculum topic:  Algebra

Curriculum subtopic:  Generate Terms of a Sequence

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

An arithmetic sequence or progression is a sequence of numbers in which the difference between consecutive terms is constant.

This means that the gap between the numbers is constant, so the numbers go up by the same amount each time, or down by the same amount each time.

 

5, 8, 11, 14, 17, 20 ...

is an arithmetic sequence in which the common difference is 3.

 

15, 11, 7, 3, -1, -5, -9 ...

is an arithmetic sequence in which the common difference is -4.

 

Example

Work out the missing term in this arithmetic sequence:

23, 18, 13, 8, 3, ?, -7, -12 ...

 

Answer

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

18 - 23 = 5

13 - 18 = -5

8 - 13 = - 5

 

The common difference is -5, so the missing term is

3 - 5 = -2

 

Work out the missing term in this arithmetic sequence:

7, 11, 15, 19, ?, 27, 31 ...

Work out the missing term in this arithmetic sequence:

1, 12, 23, ?, 45, 56...

Work out the missing term in this arithmetic sequence:

12, 22, ?, 42, 52...

Work out the missing term in this arithmetic sequence:

33, 22, ?, 0, -11...

Work out the missing term in this arithmetic sequence:

36, 27, ?, 9, 0...

Work out the missing term in this arithmetic sequence:

43, 36, 29, ?, 15, 8...

Work out the missing term in this arithmetic sequence:

-12, -8, -4, ?, 4, 8...

Work out the missing term in this arithmetic sequence:

-12, ?, -2, 3 ...

Work out the missing term in this arithmetic sequence:

-3, ?, -11, -15 ...

Work out the missing term in this arithmetic sequence:

5, ?, -9, -16 ...

  • Question 1

Work out the missing term in this arithmetic sequence:

7, 11, 15, 19, ?, 27, 31 ...

CORRECT ANSWER
23
  • Question 2

Work out the missing term in this arithmetic sequence:

1, 12, 23, ?, 45, 56...

CORRECT ANSWER
34
  • Question 3

Work out the missing term in this arithmetic sequence:

12, 22, ?, 42, 52...

CORRECT ANSWER
32
  • Question 4

Work out the missing term in this arithmetic sequence:

33, 22, ?, 0, -11...

CORRECT ANSWER
11
  • Question 5

Work out the missing term in this arithmetic sequence:

36, 27, ?, 9, 0...

CORRECT ANSWER
18
  • Question 6

Work out the missing term in this arithmetic sequence:

43, 36, 29, ?, 15, 8...

CORRECT ANSWER
22
  • Question 7

Work out the missing term in this arithmetic sequence:

-12, -8, -4, ?, 4, 8...

CORRECT ANSWER
0
  • Question 8

Work out the missing term in this arithmetic sequence:

-12, ?, -2, 3 ...

CORRECT ANSWER
-7
  • Question 9

Work out the missing term in this arithmetic sequence:

-3, ?, -11, -15 ...

CORRECT ANSWER
-7
  • Question 10

Work out the missing term in this arithmetic sequence:

5, ?, -9, -16 ...

CORRECT ANSWER
-2
---- OR ----

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