# Find and Apply Sequence Rules (Addition and Subtraction)

In this worksheet, students will identify missing numbers in sequences. These sequences may be going up or down by the same number, different numbers or multiplying by the same number.

Key stage:  KS 2

Curriculum topic:   Verbal Reasoning

Curriculum subtopic:   Number Sequences

Difficulty level:

### QUESTION 1 of 10

Hi number detective, are we glad to see you!

We’re faced with a new puzzle and we hope you can help us solve it.

Can you work out which number comes next in this sequence?

21, 25, 29, 33, __

Did you get 37?

This sequence is adding 4 each time, so when you add 4 to 33, the next number would be 37.

Which number would be next in this sequence?

9, 10, 12, 15, __

This is a changing number sequence as the amount the sequence is going up or down in changes with each step.

Can you use your number detective skills to work out what is happening in the sequence below?

2, 4, 8, 16, 32, __

The correct answer is 64. This is because the numbers are doubling (or multiplying by 2) each time. So 32 x 2 = 64.

It is now your mission to identify the missing numbers in sequences just like the ones that we have just looked at. Watch out for any sneaky changing number sequences!

Write down the relationship between the numbers as you go, it will make it easier to spot a pattern.

Good luck number detective!

We are counting on you...

Which rule is the sequence below following?

19, 23, 27, 31, 34

Which rule is the sequence below following?

19, 22, 25, 28, 31

Which rule is the sequence below following?

17, 14, 11, 8, 5

Subtract 3 each time

Subtract 2 each time

Which number would come next in this sequence?

34, 39, 44, 49, 54, __

Which number would come next in this sequence?

Fill in the blank.

Which number would come next in this sequence?

89, 86, 83, 80, __

Which number comes next in the following sequence?

Fill in the blank.

Which number would come next in this sequence?

20, 27, 34, 41, __

Match the number sequences below to their rules.

## Column B

27, 30, 33, 36
19, 28, 37, 46
Subtract 3 each time
56, 53, 50, 47

Match the sequences below to their rules.

## Column B

12, 28, 38, 48
Subtract 4 each time
19, 16, 13, 10
Subtract 3 each time
22, 18, 14, 10
• Question 1

Which rule is the sequence below following?

19, 23, 27, 31, 34

EDDIE SAYS
Hey there number detective! Did you notice that all of these numbers are 4 apart? This means that we need to add four each time to get to the next number in the sequence. So the rule is 'add 4 each time'.
• Question 2

Which rule is the sequence below following?

19, 22, 25, 28, 31

EDDIE SAYS
How much do we add to get from one number to the next? We add three! Make sure you count carefully from one number to the next to be a top number detective.
• Question 3

Which rule is the sequence below following?

17, 14, 11, 8, 5

Subtract 3 each time
EDDIE SAYS
Did you spot the pattern here? Each time the numbers are getting 3 smaller. What would be the next number in the sequence?
• Question 4

Which number would come next in this sequence?

34, 39, 44, 49, 54, __

59
EDDIE SAYS
Did you spot the rule here? The numbers are getting bigger each time, which means we are adding. Each number is 5 more than the one before it. 5 more than 54 is 59. You may have noticed that half the numbers end in a 9 and half of them end in a 4. This tells us that the pattern is staying the same and is not a changing number sequence.
• Question 5

Which number would come next in this sequence?

Fill in the blank.

EDDIE SAYS
Now this question is a challenge as the numbers are quite far apart! We are adding 8 each time here. So 8 more than 41 is 49. I find a quick way to add 8 is to add 10 and then take 2 off. How did you do it?
• Question 6

Which number would come next in this sequence?

89, 86, 83, 80, __

77
EDDIE SAYS
Did you count carefully from the first number to the second number? The numbers are getting 3 smaller each time. This means we need to take 3 away from 80. This gives us 77.
• Question 7

Which number comes next in the following sequence?

Fill in the blank.

EDDIE SAYS
Did you spot the pattern here? The numbers are getting 4 smaller each time. If we take 4 away from 22, we get 18.
• Question 8

Which number would come next in this sequence?

20, 27, 34, 41, __

48
EDDIE SAYS
Did you notice that the numbers are getting 7 bigger each time? 7 more than 41 is 48. Keep up the careful counting detective!
• Question 9

Match the number sequences below to their rules.

## Column B

27, 30, 33, 36
19, 28, 37, 46
56, 53, 50, 47
Subtract 3 each time
EDDIE SAYS
How many matches did you find? If you count carefully from one number to the next, you'll have no problem finding the rule. Just remember that if the numbers are getting smaller...it's a subtraction sequence.
• Question 10

Match the sequences below to their rules.

## Column B

12, 28, 38, 48
19, 16, 13, 10
Subtract 3 each time
22, 18, 14, 10
Subtract 4 each time
EDDIE SAYS
Did you find all the matches? Remember to look out for an addition sequence if the numbers increase, and a subtraction sequence is they decrease. Well done for your careful counting today number detective!
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