Generating sequences - Edexcel GCSE Maths (Calculator) Exam Questions

Practise 18 exam-style questions on Generating sequences for Edexcel GCSE Maths (Calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

18 questions
1–5 marks each
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18 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

The first term of a sequence is 2.5
The term-to-term rule is "multiply by 1.6 and then subtract 1".

Work out the 4th term of the sequence.

Model answer

2nd term: \(2.5 \times 1.6 - 1 = 3\)
3rd term: \(3 \times 1.6 - 1 = 3.8\)
4th term: \(3.8 \times 1.6 - 1 = 5.08\)

Explanation

A term-to-term rule tells you how to get from one term to the next, so apply it three times to get from the 1st term to the 4th term. Do the operations in the order given: multiply first, then subtract.

Mark scheme

1 mark
M1 for the 2nd and 3rd terms, 3 and 3.8
or for applying the rule correctly twice; correct answer with no working scores full marks
1 mark
A1 for 5.08
cao

Question 2

2 marks

The \(n\)th term of a sequence is \(4n^2 - 1\)

Jess says, "The 5th term of the sequence is 399."

Jess is wrong.
Explain the mistake she has made, and work out the correct 5th term.

Model answer

Jess worked out \((4 \times 5)^2 - 1 = 400 - 1 = 399\).
In \(4n^2\) only \(n\) is squared:
\(4 \times 5^2 - 1 = 4 \times 25 - 1 = 99\)
The 5th term is 99.

Explanation

By the order of operations, powers come before multiplication, so \(4n^2\) means \(4 \times n^2\), not \((4n)^2\). Square 5 first to get 25, then multiply by 4 and subtract 1.

Mark scheme

1 mark
C1 for explaining that she has squared \(4 \times 5\) (worked out \((4n)^2 - 1\)) instead of squaring only \(n\)
oe, e.g. "she did \(20^2 - 1\)"
1 mark
B1 for 99
cao

Question 3

3 marks

The term-to-term rule for a sequence is "multiply by 1.5 and then add 3".
The 4th term of the sequence is 34.5

Work out the first term of the sequence.

Model answer

Work backwards: subtract 3, then divide by 1.5
3rd term \(= (34.5 - 3) \div 1.5 = 21\)
2nd term \(= (21 - 3) \div 1.5 = 12\)
1st term \(= (12 - 3) \div 1.5 = 6\)
Check: 6, 12, 21, 34.5

Explanation

To go backwards through a term-to-term rule, use the inverse operations in the reverse order: subtract 3 first, then divide by 1.5. A common mistake is to divide first and then subtract. Check your answer by applying the rule forwards from the first term.

Mark scheme

1 mark
M1 for using the inverse operations, "subtract 3 and then divide by 1.5", e.g. \(\dfrac{34.5 - 3}{1.5} = 21\)
oe, e.g. forming \(1.5x + 3 = 34.5\); correct answer with no working scores full marks
1 mark
M1 for the 3rd and 2nd terms, 21 and 12
1 mark
A1 for 6
cao

Question 4

4 marks

Pattern number \(n\) in a sequence of patterns is made from \(5n + 3\) sticks.

Ben has 250 sticks.
He makes pattern number 1, then pattern number 2, then pattern number 3, and so on, until he does not have enough sticks left to make the next pattern.

How many patterns does Ben make, and how many sticks does he have left over?

Model answer

Sticks: 8, 13, 18, 23, 28, 33, 38, 43, 48, ...
Running totals: 8, 21, 39, 62, 90, 123, 161, 204
After 8 patterns Ben has used 204 sticks and has \(250 - 204 = 46\) left.
Pattern 9 needs \(5 \times 9 + 3 = 48\) sticks, which is more than 46.
Ben makes 8 patterns and has 46 sticks left over.

Explanation

Generate the terms from the position-to-term rule and keep a running total of the sticks used. Stop when the next pattern needs more sticks than are left. A common mistake is to solve \(5n + 3 = 250\), which finds a single pattern with 250 sticks rather than the total used by all the patterns.

Mark scheme

1 mark
P1 for the numbers of sticks in the patterns, 8, 13, 18, 23, ...
at least the first four correct; correct answer with no working scores full marks
1 mark
P1 for a running total, e.g. 8, 21, 39, 62, 90, 123, 161, 204
oe, e.g. a correct total of 204 for 8 patterns
1 mark
A1 for 8 patterns
cao
1 mark
A1 for 46 sticks left over
cao

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