A-level · Sequences & series

Arithmetic sequences and seriesExam-style questions

Sequences with a constant common difference — the nth-term rule and the sum formula, and where each comes from.

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34 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The sequence $3, 7, 11, 15, \dots$ is arithmetic.
(a) Find an expression for the $n$ th term.
(b) Hence find the $50$ th term.
Level 2 · 3 marksTry it
2
An arithmetic sequence has first term $8$ and common difference $5$ .
(a) Find an expression for the $n$ th term. (2 marks)
(b) Find the $20$ th term. (1 mark)
Level 2 · 3 marksTry it
3
Find the sum of the first $30$ terms of the arithmetic series

$2 + 9 + 16 + 23 + \cdots$ (3 marks)
Level 2 · 3 marksTry it
4
The $n$ th term of an arithmetic sequence is $u_{n} = 4n - 1$ .

Find the value of $n$ for which $u_{n} = 199$ . (3 marks)
Level 2 · 3 marksTry it
5
The third term of an arithmetic sequence is $13$ and the seventh term is $29$ .
(a) Find the first term and the common difference. (2 marks)
(b) Find the sum of the first $20$ terms. (2 marks)
Level 2 · 4 marksTry it

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