A number sequence is a list of numbers arranged in a row. Let us look at two examples below.

(i) 4, 6, 1, 10, 14, 5, …

(ii) 4, 7, 10, 13, ….

Number sequence (i) is a list of numbers without order or pattern. You cannot tell what number comes after 5.

Number sequence (ii) has a pattern. Do you observe that each number is obtained by adding 3 to the preceding number (i.e. the number just before it)?

In this section, we will only study number sequences with patterns .

Some other examples of number sequences are:

NUMBER SEQUENCE

PATTERN

3, 6, 9, 12, ...

add 3

12, 17, 22, 27, ...

add 5

70, 65, 60, 55, ...

subtract 5

15, 19, 23, 27, …

add 4

81, 27, 9, 3, …

divide by 3

Completing Missing Terms In A Number Sequence

Each of the number in the sequence is called a term.

In order to find the missing terms in a number sequence, we must first find the pattern of the number sequence.

Example :

Find the missing term in the following sequence:

8, ______, 16, ______, 24, 28, 32

Solution:

To find the pattern, look closely at 24, 28 and 32. Each term in the number sequence is formed by adding 4 to the preceding number. So, the missing terms are 8 + 4 =12 and 16 + 4 = 20. Check that the pattern is correct for the whole sequence from 8 to 32.

Example :

What is the value of n in the following number sequence?

16, 21, n, 31, 36

Solution:

We find that the number pattern of the sequence is “add 5” to the preceding number. So, n = 21 + 5 = 26

Finding The Next Term In A Number Sequence

The following video shows some examples of how to determine the next term in a number sequence.

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