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Generating sequences worksheet — GCSE Foundation

Fifteen questions on "generating sequences" — DfE statement A23. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Generating sequences worksheet — GCSE Foundation

Maths · GCSE Foundation · A23 · Generating sequences · Non-calculator · 15 questions

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1.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.
(a)20
(b)81
(c)100
(d)1000
2.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.
(a)22
(b)21
(c)25
(d)20
3.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.
(a)29
(b)25
(c)28
(d)16
4.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.
(a)52
(b)67
(c)39
(d)17
5.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.
(a)25
(b)28
(c)27
(d)31
6.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.
(a)33
(b)65
(c)32
(d)17
7.A sequence has the position-to-term rule: the nth term is 3n. Write down the first four terms of the sequence.
(a)0, 3, 6, 9
(b)3, 6, 9, 12
(c)4, 5, 6, 7
(d)3, 9, 27, 81
8.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.
(a)11
(b)−11
(c)1
(d)8
9.Which of these rules generates the sequence 6, 11, 16, 21, …?
(a)6n
(b)5n − 1
(c)5n + 1
(d)n + 5
10.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?
(a)30
(b)27
(c)28
(d)20
11.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.
(a)43
(b)37
(c)25
(d)31
12.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.
(a)28
(b)38
(c)32
(d)33
13.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?
(a)No: the 8th term is 50 − 8 × 6 = 2, which is positive.
(b)Yes, but the 8th term is 50 − 8 × 8 = −14.
(c)No: repeated subtraction from 50 can never go negative.
(d)Yes: the 8th term is 50 − 8 × 7 = −6, which is negative.
14.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.
(a)11
(b)7
(c)9
(d)12
15.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.
(a)8
(b)64
(c)16
(d)81

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