Number Sequences
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How to Find The Next Term In A Number Sequence?
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 |
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
The following video shows some examples of how to determine the next term in a number sequence.
Examples:
Find the next number
1. 1, 8, 15, 22, ...
2. 1, 8, 64, 512, ...
3. 1, 8, 27, 64, ....
4. 1, 8, 16, 15, ... The following diagrams give the formulas for Arithmetic Sequence and Geometric Sequence. Scroll down the page for examples and solutions.
Example:
7, 9, 11, 13, 15, ... How to find the nth Term of a Geometric Sequence?
Example:
5, 10, 20, 40, ...
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