Understand the rule first
Write the change between every pair of terms. If the changes do not repeat, test alternating rules, multiplication or a rule based on the term position.
Number sequences 11+ practice
Recognise constant, alternating and position-based number sequence rules.
Find the next term: 7, 12, 17, 22, __.
- The differences are +5, +5 and +5.
- Apply the same constant difference.
- 22 + 5 = 27.
A common misconception
Using only the final difference instead of checking that a rule explains every term.
Reusable method: Write the change between every pair of terms.Question 1 of 8 MathscoreWhat comes next: 2, 6, 10, 14, __?
- A18
- B16
- C20
- D22
Need a hint?
Compare consecutive terms.
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Answer A: 18
Each term increases by 4, so 14 + 4 = 18.
Quick method: Write the change between every pair of terms.
Question 2 of 8 MathscoreWhat comes next: 81, 27, 9, 3, __?
- A0
- B1
- C2
- D6
Need a hint?
Each term is obtained by the same division.
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Answer B: 1
Each term is divided by 3, so 3 ÷ 3 = 1.
Quick method: Write the change between every pair of terms.
Question 3 of 8 MathscoreWhat comes next: 5, 9, 8, 12, 11, __?
- A12
- B14
- C15
- D16
Need a hint?
The changes alternate +4, −1.
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Answer C: 15
After 11, the +4 step gives 15.
Quick method: Write the change between every pair of terms.
Question 4 of 8 Mathsexam-styleThe nth term of a sequence is 3n + 2. What is the 12th term?
- A17
- B34
- C36
- D38
Need a hint?
Substitute 12 for n.
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Answer D: 38
3 × 12 + 2 = 36 + 2 = 38.
Quick method: Write the change between every pair of terms.
Question 5 of 8 Mathsexam-styleWhat comes next: 1, 3, 6, 10, 15, __?
- A21
- B19
- C20
- D22
Need a hint?
The differences are consecutive whole numbers.
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Answer A: 21
The sequence adds 2, 3, 4 and 5; adding 6 gives 21.
Quick method: Write the change between every pair of terms.
Question 6 of 8 Mathsexam-styleWhat comes next: 1, 4, 9, 16, 25, __?
- A36
- B30
- C32
- D49
Need a hint?
These are square numbers.
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Answer A: 36
The terms are 1², 2², 3², 4² and 5², so the next is 6² = 36.
Quick method: Write the change between every pair of terms.
Question 7 of 8 Mathsexam-styleThe nth term is 5n − 2. What is the 9th term?
- A35
- B43
- C45
- D47
Need a hint?
Substitute 9 for n.
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Answer B: 43
5 × 9 − 2 = 45 − 2 = 43.
Quick method: Write the change between every pair of terms.
Question 8 of 8 Mathsexam-styleWhat comes next: 100, 50, 55, 27.5, 32.5, __?
- A13.75
- B15
- C16.25
- D27.5
Need a hint?
The operations alternate ÷2, +5.
Show worked answer
Answer C: 16.25
After 32.5 the divide-by-two step gives 16.25.
Quick method: Write the change between every pair of terms.