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Sequences (nth term) practice questions with answers

Foundation and Higher · Grade 4 · Non-calculator

A second set of sequences (nth term) 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 1 Easy

An arithmetic sequence starts at 5 and goes up by 3. What is the 8th term?

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Answer: 26

  1. Seven steps of 3 come after the first term.
  2. 5 + 21.
  • Method (1): Seven steps of 3 come after the first term.
  • Accuracy (1): Answer 26

Question 2 Easy

The nth term is 4n − 1. What is the first term?

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Answer: 3

  1. Put n = 1 into the rule.
  2. The value is 3.
  • Method (1): Put n = 1 into the rule.
  • Accuracy (1): Answer 3

Question 3 Medium

Sequence A has nth term 2n. Sequence B has nth term n + 6. For which n are the terms equal?

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Answer: 6

  1. Set 2n = n + the constant.
  2. Solve for n.
  • Method (1): Set 2n = n + the constant.
  • Accuracy (1): Answer 6

Question 4 Medium

The first term is 4 and the fourth term is 19. What is the common difference?

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Answer: 5

  1. Three steps separate the first and fourth terms.
  2. Divide the gap by 3.
  • Method (1): Three steps separate the first and fourth terms.
  • Accuracy (1): Answer 5

Question 5 Hard

The nth term is 4n + 1. How much greater is the 10th term than the 7th term?

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Answer: 12

  1. The constant cancels.
  2. Three steps of 4 make the gap.
  • Method (1): The constant cancels.
  • Accuracy (1): Answer 12

Question 6 Hard

A taxi costs £3 plus £2 per mile. What does a 8 mile journey cost?

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Answer: 19

  1. The miles use the ×2 part.
  2. Then add the fixed charge.
  • Method (1): The miles use the ×2 part.
  • Accuracy (1): Answer 19

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 arithmetic sequence 5, 8, 11 has common difference 3. Find the 20th term.

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Answer: 62

  1. Nineteen steps of 3 come after the first term.
  2. 5 + 57.
  • Method (1): Nineteen steps of 3 come after the first term.
  • Accuracy (1): Answer 62

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A sequence starts at 23 and increases by 2 each time. What is term 4?

  1. 29
  2. 31
  3. 6
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29 The result is 29.

Check 2

Find the nth term of the sequence 1, 4, 7, 10, ...

  1. 3n-2
  2. 3n
  3. 3n+2
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3n-2 The result is 3n-2.

Check 3

The nth term of a sequence is 4n + 2. Work out the 15th term.

  1. 62
  2. 60
  3. 58
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62 The result is 62.

Check 4

The nth term of a sequence is 5n + 5. Which term of the sequence is equal to 25? Give the value of n.

  1. 4
  2. 20
  3. 6
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4 The result is 4.

Check 5

A sequence starts at 27 and increases by 2 each time. What is term 8?

  1. 41
  2. 43
  3. 14
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41 The result is 41.

Check 6

Find the nth term of the sequence 4, 6, 8, 10, ...

  1. 2n+2
  2. 2n
  3. 2n-2
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2n+2 The result is 2n+2.

Check 7

The nth term of a sequence is 3n − 6. Work out the 8th term.

  1. 18
  2. 24
  3. 30
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18 The result is 18.

Check 8

The nth term of a sequence is 4n + 6. Which term of the sequence is equal to 18? Give the value of n.

  1. 3
  2. 12
  3. 6
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3 The result is 3.

Check 9

A sequence starts at 31 and increases by 2 each time. What is term 7?

  1. 43
  2. 45
  3. 12
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43 The result is 43.

Check 10

Find the nth term of the sequence 7, 13, 19, 25, ...

  1. 6n+1
  2. 6n
  3. 6n-1
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6n+1 The result is 6n+1.

Check 11

The nth term of a sequence is 2n + 5. Work out the 15th term.

  1. 35
  2. 30
  3. 25
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35 The result is 35.

Check 12

The nth term of a sequence is 3n − 4. Which term of the sequence is equal to 29? Give the value of n.

  1. 11
  2. 33
  3. 8.33
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11 The result is 11.

Check 13

A sequence starts at 35 and increases by 2 each time. What is term 6?

  1. 45
  2. 47
  3. 10
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45 The result is 45.

Check 14

Find the nth term of the sequence 1, 6, 11, 16, ...

  1. 5n-4
  2. 5n
  3. 5n+4
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5n-4 The result is 5n-4.

Check 15

The nth term of a sequence is 6n + 1. Work out the 8th term.

  1. 49
  2. 48
  3. 47
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49 The result is 49.

Keep going with Sequences (nth term)

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