GCSE · Sequences

Geometric, Fibonacci and other special sequencesExam-style questions

Why geometric sequences multiply where arithmetic ones add, how Fibonacci-type rules turn into algebra, the named sequences worth recognising on sight, and subscript notation for term-to-term rules.

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15 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
The first two terms of a Fibonacci-type sequence are $a$ and $b$ .

Each term after the second is the sum of the two previous terms.

The 4th term of the sequence is 10.

The 5th term of the sequence is 17.

Work out the values of $a$ and $b$ .
Level 5 · 3 marksTry it
2
The first two terms of a Fibonacci-type sequence are $p$ and $q$ . Each term after the second is the sum of the two previous terms.

The $3$ rd term is $11$ and the $5$ th term is $29$ .

Work out the values of $p$ and $q$ .
Level 5 · 4 marksTry it
3
A council recycled $960$ tonnes of plastic in 2024 and $1200$ tonnes of plastic in 2025.

The council uses the model

$R_{n+1} = KR_n$

where $R_n$ is the number of tonnes of plastic it recycles in year $n$ and $K$ is a constant.

Use the model to show that the council will recycle more than $2300$ tonnes of plastic in 2028.

(3 marks)
Level 5 · 3 marksTry it
4
Here are the first three terms of an arithmetic sequence.

$5k - 2 \qquad 2k + 9 \qquad 3k + 4$
(a) Find the value of $k$ .

(2 marks)

Here are the first three terms of a geometric sequence.

$2p - 5 \qquad 2p + 1 \qquad 5p + 7$
(b) Find the possible values of $p$ .

(5 marks)
Level 5 · 7 marksTry it