 What you need to know

Things to remember:

• Compare the difference between multiple pairs of numbers to see if it is going up by the same amount.
• We need to be careful numbers, especially when finding the difference between a pair of numbers where one is positive, and the other is negative.

Here we are going to be looking at sequences of integers and finding missing numbers.

Find the missing number in the following sequence:

5                      10                    15                    ___                  25

We can do this in two steps:

Step 1: Choose two pairs of numbers that are next to each other and subtract the smallest from the biggest.

$$10-5=5$$

$$15-10=5$$

So, the difference is 5.

Step 2: Add or subtract the difference found in Step 1 to the number before the missing number.

Our numbers are increasing, so we want to add this difference.

$$15 + 5=20$$

So, the missing number is 20.

Check: We can use this number in Step 1 to check that the difference is the same.

$$25-20=5$$

This is the same difference, so our check tells us that our answer is correct!

How about when the number are decreasing? We can use the same steps.

Find the missing number in the following sequence:

5                      1                      -3                     -7                     ___

Step 1: Choose two pairs of numbers that are next to each other and subtract the smallest from the biggest.

Hint: When we subtract a negative number, it becomes an add!

Hint: The “bigger” the number part of a negative number, the smaller it is.

$$5-1=4$$

$$-3- -7=-3+7=4$$

So, the difference is 4.

Step 2: Add or subtract the difference found in Step 1 to the number before the missing number.

Our numbers are decreasing, so we want to subtract this difference.

$$-7 -4 =-11$$

So, the missing number is -11.

Check: We can use this number in Step 1 to check that the difference is the same.

$$-7--11=-7+11=4$$

This is the same difference, so our check tells us that our answer is correct!

Example Questions

Step 1: Choose two pairs of numbers that are next to each other and subtract the smallest from the biggest.

$$30-24=6$$

$$24-18=6$$

So, the difference is 6.

Step 2: Add or subtract the difference found in Step 1 to the number before the missing number.

Our numbers are increasing, so we want to add this difference.

$$6 + 6=12$$

So, the missing number is 12.

Check: We can use this number in Step 1 to check that the difference is the same.

$$18 - 12=6$$

This is the same difference, so our check tells us that our answer is correct!

Step 1: Choose two pairs of numbers that are next to each other and subtract the smallest from the biggest.

Hint: When we subtract a negative number, it becomes an add!

Hint: The “bigger” the number part of a negative number, the smaller it is.

$$-3--5=-3+5=2$$

$$-1--3=-1+3=2$$

So, the difference is 2.

Step 2: Add or subtract the difference found in Step 1 to the number before the missing number.

Our numbers are decreasing, so we want to subtract this difference.

$$-5 -2 =-7$$

So, the missing number is -7.

Check: We can use this number in Step 1 to check that the difference is the same.

$$-5--7=-5+7=2$$

This is the same difference, so our check tells us that our answer is correct!