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
Here are the first four terms of a geometric sequence:

$\sqrt{3} \qquad 3 \qquad 3\sqrt{3} \qquad 9$

Work out the next term of the sequence.

Give your answer in its simplest surd form.
Level 4 · 2 marksTry it
2
A sequence is defined by

$x_{n+1} = 3x_n - 2, \qquad x_1 = 4$

Work out the values of $x_2$ and $x_3$ .
Level 4 · 2 marksTry it
3
Here are the first four terms of a geometric sequence:

$80 \qquad 40 \qquad 20 \qquad 10$

Work out the $7$ th term of the sequence.
Level 4 · 2 marksTry it
4
Here are the first four terms of a geometric sequence:

$2 \qquad 2\sqrt{5} \qquad 10 \qquad 10\sqrt{5}$

Work out the $5$ th term of the sequence.
Level 4 · 2 marksTry it
5
A scientist is growing bacteria in a dish.

$B_n$ is the number of bacteria in the dish at the end of day $n$ .

$B_{n+1} = 1.5B_n$

At the end of day $2$ there are $3200$ bacteria in the dish.

Work out the number of bacteria in the dish at the end of day $5$ .

(3 marks)
Level 4 · 3 marksTry it