(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 |
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