Subtract a number each time
for 3rd grade

Number patterns: subtract the same number each time

This topic explores number patterns that involve subtracting the same number each time. This type of sequence of numbers is known as a descending arithmetic sequence because it changes by the same amount each time and gets smaller each time. Let's start by looking at a simple number pattern:

12 , 10 , 8 , 6 , _ , _ ...

What comes next? To find out, let's first look at the differences between each pair of numbers:

• 10 - 12 = -2
• 8 - 10 = -2
• 6 - 8 = -2

You can see that in each step, we take away 2 from the previous number to get the next number in the sequence. Now, let's use this rule to find the next number:

6 - 2 = 4

So, the next number in the pattern is 4. The sequence now looks like this:

12 , 10 , 8 , 6 , 4 , _ ...

If we do the next number in the sequence, it will be 4 - 2 which is 2,

12 , 10 , 8 , 6 , 4 , 2 ...

So always remember the following steps when identifying the next number in a pattern that subtracts the same number each time:

1. Identify the difference between each pair of numbers.
2. Subtact this difference from the last number in the sequence.
3. That gives you the next number in the sequence.

This topic asks you to work out the missing number in the pattern of numbers created by taking away the same number each time.

Related topics

• Add a number each time
• Double a number each time