# 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?

16, 22, 28, 34, 40

Which rule is the sequence below following?

13, 23, 33, 43, 53

Subtract 10 each time

Which rule is the sequence below following?

30, 27, 24, 21, 18

Subtract 4 each time

Subtract 3 each time

Which number would come next in the sequence below?

12, 19, 26, 33, 40, __

Which number would come next in the sequence below?

Fill in the blank.

Which number would come next in the following sequence?

30, 28, 26, 24, __

Which number would come next in the sequence?

Fill in the blank.

Which number would come next in the following sequence?

98, 88, 78, 68, __

Match the sequences to their rules.

## Column B

33, 43, 53, 63
Subtract 2 each time
27, 25, 23, 21
Subtract 3 each time
35, 39, 43, 47
49, 46, 43, 40

Match the sequences to their final numbers.

## Column B

31, 35, 39, 43
61
54, 51, 48, 45
42
67, 69, 71, 73
47
101, 91, 81, 71
75
• Question 1

Which rule is the sequence below following?

16, 22, 28, 34, 40

EDDIE SAYS
Hey there number detective! How much do we need to add to get from one number to the next? All of the numbers are 6 apart. This means that the rule is 'add 6 each time'.
• Question 2

Which rule is the sequence below following?

13, 23, 33, 43, 53

EDDIE SAYS
Did you use your detective skills to spot the rule here? We are adding 10 more each time to get to the next number. Another way to think about this is that the difference between each number in the sequence is 10.
• Question 3

Which rule is the sequence below following?

30, 27, 24, 21, 18

Subtract 3 each time
EDDIE SAYS
Our numbers are getting smaller each time here! This means that we are subtracting. How much smaller are the numbers getting? They are getting 3 smaller, which means the rule is 'subtract 3 each time'. I'm counting on you to count carefully number detective!
• Question 4

Which number would come next in the sequence below?

12, 19, 26, 33, 40, __

47
EDDIE SAYS
Did you notice that the numbers were getting 7 bigger each time? This means that we have to add 7 more to 40. This means that 47 is the next number in the sequence.
• Question 5

Which number would come next in the sequence below?

Fill in the blank.

EDDIE SAYS
How much were we adding each time here? Each number is 4 more than the one before it. If we add 4 more to 35, we get 39. Count carefully from each number to the next and this will help you work out the rule.
• Question 6

Which number would come next in the following sequence?

30, 28, 26, 24, __

22
EDDIE SAYS
The numbers are getting smaller here! This means that we need to subtract to find the next number. Each number is 2 smaller than the one before it. So we need to take away 2 from 24. This gives us the answer of 22.
• Question 7

Which number would come next in the sequence?

Fill in the blank.

EDDIE SAYS
We have another sequence that's getting smaller! How much smaller is it getting each time? Each number is 4 less than the number before it. 4 less than 39 is 34.
• Question 8

Which number would come next in the following sequence?

98, 88, 78, 68, __

58
EDDIE SAYS
Did you notice that all of the numbers in this sequence end in 8? It is only the number in the tens column that is changing. We are subtracting 10 each time here. 10 less than 68 is 58.
• Question 9

Match the sequences to their rules.

## Column B

33, 43, 53, 63
27, 25, 23, 21
Subtract 2 each time
35, 39, 43, 47
49, 46, 43, 40
Subtract 3 each time
EDDIE SAYS
How many matches did you find number detective? If the numbers are getting bigger, we are adding. If the numbers are getting smaller, we are subtracting.
• Question 10

Match the sequences to their final numbers.

## Column B

31, 35, 39, 43
47
54, 51, 48, 45
42
67, 69, 71, 73
75
101, 91, 81, 71
61
EDDIE SAYS
Did you count carefully to work out the rules of these sequences? In the first sequence we were adding 4 and 4 more than 43 is 47. In the second sequence, we were subtracting 3 and 3 less than 45 is 42. In the third sequence, we were adding 2 and 2 more than 73 is 75. In the final sequence, we were subtracting 10 and 10 less than 71 is 61. I knew I could COUNT on you!
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