# Identifying number patterns

## Identifying and completing number patterns

With practice, a variety of common number patterns can be identified. This requires careful observation. Identifying patterns involves being able to look at features such as differences (the amounts between numbers) and rates of change (how quickly the numbers are seen to increase or decrease).

Often, a pattern will start and you will be required to continue the series. You can do this by first identifying the pattern and then making use of the last number to extend the sequence.

Examples:

2, 5, 8, 11, 14, 17, ..., ... addition (+ 3)

100, 96, 92, 88, 84, ..., ... subtraction (- 4)

2, 4, 8, 16, 32, 64, ..., ... multiplication (doubling)

160, 80, 40, 20, 10, ..., ... division (halving)

81, 64, 49, 36, 25, ..., ... decreasing square numbers

Sometimes the missing numbers may be located within the number sequence. You can use the surrounding numbers as a guide.

Examples:

14, 26, ..., 50, ..., 74, 86 addition (+ 12)

93, 82, 71, ..., ..., 38, 27 subtraction (- 11)

1, ..., ..., 125, 625, 3 125 multiplication (x 5)

1 000, ..., 10, 1, ..., 0.01 division ( 10)

## Number patterns within tables

Sometimes you may be provided with a table or grid which has a series of numbers and a rule to follow. Provided the series of numbers given is already an uninterrupted sequence, the answers which complete the grid should form a pattern.

Example:

The answers to this grid (90, 140, 190, 240, 290 and 340) maintain the pattern which has already been established.

## Identifying the rule and completing the pattern

You might be given a sequence of paired numbers and asked to identify a rule for the pattern. You may also then be asked to complete the sequence.

Example:

You must work out what number operation has been used to create the pattern and then use the rule to calculate the missing values in the pattern.

## Patterns and problem solving

We can also make use of patterns for solving problems. Being able to identify patterns can save a great deal of time in working out a solution to a problem.

*See animation*