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Ask yourself: Do the numbers in this number pattern increase in value (go up) or decrease in value (go down)?

If the numbers increase, do they increase by the same amount each time?
If the numbers decrease, do they decrease by the same amount each time?

Example 1

In the example below, the numbers are increasing.

1, 13, 25, 37, 49, …

What do you need to add to each number to get to the next number in the pattern?

You need to add 12 to get from one number to the next. This is shown below.

1 + 12 = 13, 13 + 12 = 25, 25 + 12 = 37, 37 + 12 = 49,

To find the next number in the pattern we need to add 12 to 49. Therefore, the next number in this number pattern is 61.

Example 2

In the example below, the numbers are decreasing.

107, 100, 93, 86, ...

What do you need to subtract from each number to get to the next number in the pattern?

You need to subtract 7 to get from one number to the next. This is shown below.

107 - 7 = 100, 100 - 7 = 93, 93 - 7 = 86

So, to find the next number in the pattern we will need to subtract 7 from 86. Our answer is 79.


Now, what if the numbers in your pattern do not increase, or decrease, by the same amount each time? The number pattern may involve multiplication or division.

If the numbers in your pattern are increasing (going up): Is there a number that you can multiply each number by, to get you to the next number in the pattern?

If the numbers in your pattern are decreasing (going down): Is there a number that you can divide each number by, to get you to the next number in the pattern?

Example 3

The numbers in the following pattern are increasing.

1, 4, 16, 64, 256, …

What number would we have to multiply 1 by, to get 4? (Answer: 4)
What number would we have to multiply 4 by, to get 16? (Answer: 4)
What number would we have to multiply 16 by, to get 64? (Answer: 4)
What number would we have to multiply 64 by, to get 256? (Answer: 4)

What have we discovered? That we need to multiply each number in the pattern by 4, to get to the next number in the pattern.

Therefore, to find the next number in this pattern, we will multiply 256 by 4. The next number is 1024.

Tomorrow we will discuss what you can try if none of the strategies above work for your number pattern.