Question 1 Easy
The first term of a sequence is 2 and the rule is add 6. What is the 4th term?
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Answer: 20
- Start with 2.
- 2 + 6 = 8.
- 8 + 6 = 14.
- 14 + 6 = 20.
- Method (1): Start with 2.
- Accuracy (1): Answer 20
Sequences: rules and special sequences practice questions with answers
A second set of sequences: rules and special sequences questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
More questions
Question 2 Easy
The first term of a sequence is 20 and the rule is subtract 3. What is the 5th term?
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Answer: 8
- Start with 20.
- 20 - 3 = 17.
- 17 - 3 = 14.
- 14 - 3 = 11.
- 11 - 3 = 8.
- Method (1): Start with 20.
- Accuracy (1): Answer 8
Question 3 Medium
The triangular numbers begin 1, 3, 6, 10, 15. What is the 7th triangular number?
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Answer: 28
- Each new term adds one more than the last gap: the gaps are 2, 3, 4, 5, ...
- The 7th term is 28.
- Method (1): Each new term adds one more than the last gap: the gaps are 2, 3, 4, 5, ...
- Accuracy (1): Answer 28
Question 4 Medium
The cube numbers begin 1, 8, 27, 64. What is the 5th cube number?
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Answer: 125
- The 5th cube number is 5 × 5 × 5.
- 5 × 5 × 5 = 125.
- Method (1): The 5th cube number is 5 × 5 × 5.
- Accuracy (1): Answer 125
Question 5 Medium
Each term is the sum of the two terms before it. The sequence starts 1, 3, 4, 7. What is the next term?
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Answer: 11
- Add the last two terms: 7 + 4.
- 7 + 4 = 11.
- Method (1): Add the last two terms: 7 + 4.
- Accuracy (1): Answer 11
Question 6 Hard
a sequence starts at 80 and each term is half of the one before. What is the 4th term?
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Answer: 10
- 80 ÷ 2 = 40.
- 40 ÷ 2 = 20.
- 20 ÷ 2 = 10.
- Method (1): 80 ÷ 2 = 40.
- Accuracy (1): Answer 10
Question 7 Hard
a sequence starts at 2. The rule is multiply by 3 then subtract 1. Work out the 4th term.
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Answer: 41
- 2 × 3 - 1 = 5.
- 5 × 3 - 1 = 14.
- 14 × 3 - 1 = 41.
- Method (1): 2 × 3 - 1 = 5.
- Accuracy (1): Answer 41
Exam-style question
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
Exam-style question 12 marks
The first term of a sequence is 6. The rule is add 5. Work out the 5th term.
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Answer: 26
- 6, 11, 16, 21, 26.
- Method (1): Adds 5 repeatedly, or works out 6 + 4 × 5
- Accuracy (1): 26
Quick checks
Short one-step questions. Pick an option before you open the answer.
Check 1
What is a term in a sequence?
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One number in the list. One number in the list.
Check 2
What does a term-to-term rule tell you?
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What to do to one term to get the next term. What to do to one term to get the next term.
Check 3
What does a position-to-term rule tell you?
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How to find a term from its place in the list, such as multiply the position by 3 and add 1. How to find a term from its place in the list, such as multiply the position by 3 and add 1.
Check 4
How do you find the rule for 5, 9, 13, 17?
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Subtract neighbouring terms. The gap is always 4, so the rule is add 4. Subtract neighbouring terms. The gap is always 4, so the rule is add 4.
Check 5
What are the first five square numbers?
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1, 4, 9, 16, 25. 1, 4, 9, 16, 25.
Check 6
What are the first four cube numbers?
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1, 8, 27, 64. 1, 8, 27, 64.
Check 7
What are the first five triangular numbers?
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1, 3, 6, 10, 15. The gaps go up 2, 3, 4, 5. 1, 3, 6, 10, 15. The gaps go up 2, 3, 4, 5.
Check 8
What is special about 1, 1, 2, 3, 5, 8?
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Each term is the sum of the two terms before it. Each term is the sum of the two terms before it.
Check 9
How many times do you apply the rule to get from the 1st term to the 6th term?
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Five times. Five times.
Check 10
A sequence goes down by 3 each time. What is the rule?
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Subtract 3. Subtract 3.
Check 11
What is the 5th square number?
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25, because 5 × 5 = 25. 25, because 5 × 5 = 25.
Check 12
What is the 4th cube number?
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64, because 4 × 4 × 4 = 64. 64, because 4 × 4 × 4 = 64.
Check 13
Why can a position-to-term rule be quicker than a term-to-term rule?
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You can find the 50th term without listing the 49 before it. You can find the 50th term without listing the 49 before it.
Check 14
What should you do if the gaps in a sequence are not all the same?
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Look for multiplying, or a pattern in the gaps. Look for multiplying, or a pattern in the gaps.
Check 15
What is the next term in 2, 4, 8, 16?
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32. The rule is multiply by 2. 32. The rule is multiply by 2.
Check 16
How can you check a rule you have found?
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Use it on the first few terms and see that it gives the terms in the list. Use it on the first few terms and see that it gives the terms in the list.
Keep going with Sequences: rules and special sequences
Practise free
AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.