MathsFreePrintable
Number Patterns Investigation
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Number Patterns Investigation
Read each number sequence carefully. Write the missing numbers and explain the rule when asked. For pattern-making questions, use the example answer as a guide; other correct patterns are possible.
Spot the Rule
Look for how much each number changes from one term to the next.
1.Complete the sequence 4, 8, 12, 16, __, __. State the rule.
2.Fill in the next two numbers in 42, 36, 30, 24, __, __. What is the rule?
3.Which sequence follows the rule “add 5 each time”?
- 3, 8, 13, 18, 23
- 5, 10, 20, 25, 30
- 21, 16, 11, 6, 1
- 2, 7, 11, 16, 20
4.The sequence is 64, 56, 48, 40, __. Choose the next number.
- 24
- 32
- 36
- 48
Sequence
First term
Second term
Third term
Rule
A
6
__
18
__
B
50
45
__
__
5.Complete rows A and B in the Track the Terms table. Write the rule for each row.
Build and Extend Patterns
Use repeated addition or subtraction to continue a sequence.
6.Start at 9 and add 4 each time. Write the first six terms.
7.Make a six-term sequence that starts at 48 and subtracts the same amount each time. Use 3 as the amount subtracted, then write your rule.
8.For the sequence 7, 11, 15, 19, 23, what is the rule and what is the 8th term? Show how you worked it out.
9.Match each sequence to its rule.
- 10, 15, 20, 25
- 38, 31, 24, 17
- 2, 9, 16, 23
- 60, 50, 40, 30
- Subtract 7 each time
- Subtract 10 each time
- Add 5 each time
- Add 7 each time
10.A pattern starts at 12. It adds 5, then subtracts 2, and repeats those two steps. Write the first six terms and describe the repeating rule.
11.What is one way number patterns can help you solve maths problems?
3 printable pages
Page 1
Page 2
Page 3
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