Algebra and equations · Ages 9–10
Rules for number sequences worksheet
Part of: Patterns and rules
In the print window, choose “Save as PDF” to download it. The answers print on the last page.
Rules for number sequences worksheet
Algebra and equations · Ages 9–10
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Continue the sequence: 87, 83, 79, 75,
Answer:
2.Continue the sequence: 17, 19, 21, 23,
Answer:
3.Continue the sequence: 76, 73, 70, 67,
Answer:
4.Continue the sequence: 1, 2, 4,
Answer:
5.Continue the sequence: 25, 36, 49, 64,
Answer:
6.Fill in the sequence: 7, , 25, , 43
Fill in each blank
Answer:
7.Fill in the sequence: 36, , 58, , 80
Fill in each blank
Answer:
8.Continue the sequence: 2, 6, 18,
Answer:
9.Continue the sequence: 1, 4, 9, 16,
Answer:
10.Continue the sequence: 6, 10, 15, 21,
Answer:
11.Continue the sequence: 17, 18, 20, 23,
Answer:
Part B: Choose, or true or false (2 marks each)
12.What is the rule for 6, 12, 24, 48?
- A. Add 6 each time
- B. Add 12 each time
- C. Multiply by 2 each time
- D. Multiply by 3 each time
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.May's Octopus card starts with $108. Each day May spends $14 on fares: $94 is left after day 1, $80 after day 2. If it carries on like this, how many dollars are left after day 7?
Working:
Answer:
14.Square tiles make bigger squares: a side of 1 tile needs 1, a side of 2 needs 4, a side of 3 needs 9. Going from a side of 4 tiles to a side of 5, how many more tiles are needed?
Working:
Answer:
15.Tsz-ching reads 13 pages of a storybook on day 1, and each day after reads 3 more pages than the day before. How many pages does Tsz-ching read on day 5?
Working:
Answer:
16.A ball is dropped from 96 cm. Each bounce reaches half the height of the one before, and the 1st bounce reaches 48 cm. How high is bounce 3?
Working:
Answer:
17.Ka-yee reads 11 pages of a storybook on day 1, and each day after reads 3 more pages than the day before. How many pages does Ka-yee read on day 7?
Working:
Answer:
18.Square tiles make bigger squares: a side of 1 tile needs 1, a side of 2 needs 4, a side of 3 needs 9. Going from a side of 12 tiles to a side of 13, how many more tiles are needed?
Working:
Answer:
Show the answers and working
Rules for number sequences worksheet: Answers and working
Part A: Working out and filling in
1. 71
How much less is 83 than 87? Check the other neighbours drop by the same.
Each number is 4 less than the one before, so subtract 4: 75 − 4 = 71.
2. 25
Look at the gaps: how much more is 19 than 17? Is it the same for the other neighbours?
Each number is 2 more than the one before, so add 2: 23 + 2 = 25.
3. 64
How much less is 73 than 76? Check the other neighbours drop by the same.
Each number is 3 less than the one before, so subtract 3: 67 − 3 = 64.
4. 8
The gaps keep growing, so try multiplying: 2 is how many times 1?
The gaps keep growing, so try multiplying: each number is 2 times the one before. 4 × 2 = 8.
5. 81
Look at the gaps from 25 to 36 and from 36 to 49. What pattern do the gaps follow?
The gaps are 11, 13, 15, each 2 more, so the next gap is 17: 64 + 17 = 81. They are square numbers: 81 = 9 × 9.
6. 16, 34
From 7 to 25 is two steps. Find how much it goes up in all, then split that into two equal steps.
From 7 to 25 is two steps adding 18, so each step adds 9: 7, 16, 25, 34, 43.
7. 47, 69
From 36 to 58 is two steps. Find how much it goes up in all, then split that into two equal steps.
From 36 to 58 is two steps adding 22, so each step adds 11: 36, 47, 58, 69, 80.
8. 54
The gaps keep growing, so try multiplying: 6 is how many times 2?
The gaps keep growing, so try multiplying: each number is 3 times the one before. 18 × 3 = 54.
9. 25
Look at the gaps from 1 to 4 and from 4 to 9. What pattern do the gaps follow?
The gaps are 3, 5, 7, each 2 more, so the next gap is 9: 16 + 9 = 25. They are square numbers: 25 = 5 × 5.
10. 28
Write down the gaps between neighbours, then see how the gaps change.
The gaps are 4, 5, 6, each 1 more, so the next gap is 7: 21 + 7 = 28.
11. 27
Write down the gaps between neighbours, then see how the gaps change.
The gaps are 1, 2, 3, each 1 more, so the next gap is 4: 23 + 4 = 27.
Part B: Choose, or true or false
12. C. Multiply by 2 each time
Check each rule on every pair: does the same one take 6 to 12 and 12 to 24?
6 × 2 = 12, 12 × 2 = 24, 24 × 2 = 48: every pair is × 2.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 10 dollars
How much does it drop each day? How much over 7 days?
It drops by 14 a day, so 7 days use 14 × 7 = 98: 108 − 98 = 10.
14. 9 tiles
Write down the gaps between 1, 4 and 9 and see their pattern; or draw it to see where the new tiles go.
1, 4, 9, 16, … go up by 3, 5, 7, …: from a side of 4 to 5 you add a row, a column and the corner: 4 + 4 + 1 = 9.
15. 25 pages
Between day 1 and day 5, how many times is 3 added? Careful: it isn't 5.
It goes up 3 a day. Day 5 is 4 days after day 1: 13 + 4 × 3 = 25.
16. 12 cm
Each bounce is half the one before. Start from the 1st bounce's 48 cm and halve it bounce by bounce.
The rule is ÷ 2 each time: halve 96 3 times to get 12 cm.
17. 29 pages
Between day 1 and day 7, how many times is 3 added? Careful: it isn't 7.
It goes up 3 a day. Day 7 is 6 days after day 1: 11 + 6 × 3 = 29.
18. 25 tiles
Write down the gaps between 1, 4 and 9 and see their pattern; or draw it to see where the new tiles go.
1, 4, 9, 16, … go up by 3, 5, 7, …: from a side of 12 to 13 you add a row, a column and the corner: 12 + 12 + 1 = 25.
Numsprite · numsprite.com/en/worksheets/patterns-and-rules/number-sequence-rules
Practise it in the gameRules for number sequences · Unlimited questions, no download