A-level · Sequences & series

Geometric sequences and seriesExam-style questions

Sequences with a constant common ratio — the nth term, the sum of n terms, and the sum to infinity (and exactly when it exists).

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29 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
In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

The sum to infinity of a geometric series is $64$

The sum of the first three terms of the same series is $37$
(a) Find the common ratio of the series.

(4 marks)
(b) Find the first term of the series.

(2 marks)
Level 3 · 6 marksTry it
2
Find the sum to infinity of the geometric series $8 + 4 + 2 + 1 + \dots$
Level 3 · 2 marksTry it
3
A geometric series has first term $5$ and sum to infinity $20$ . Find the common ratio $r$ .
Level 3 · 2 marksTry it
4
The $2$ nd term of a geometric series is $6$ and the $5$ th term is $48$ .
(a) Find the common ratio and the first term.
(b) Find the sum of the first $8$ terms.
Level 3 · 4 marksTry it
5
A geometric series has first term $12$ and common ratio $\tfrac23$ .
(a) Find the fifth term, to 3 s.f. (2 marks)
(b) Find the sum to infinity. (2 marks)
(c) Find the sum of the first six terms, to 3 s.f. (3 marks)
Level 3 · 7 marksTry it

6 more questions on geometric sequences and series

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