plumiGeometric sequences and series: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on D.6 Geometric sequences and series, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 11 questions on Geometric sequences and series, as a list
- June 2025, Paper 1, Q9 (10 marks): (a) A geometric series, S, has second term 60 The common ratio of S is 0.2 Find the exact value of the sum of the first five terms of S [4 marks] 9 (b) A differ
- June 2024, Paper 2, Q7 (5 marks): On the first day of each month, Kate pays £50 into a savings account. Interest is paid on the total amount in the account on the last day of each month. The int
- June 2024, Paper 2, Q9 (13 marks): (a) (i) Find the binomial expansion of (1 + 3x)–1 up to and including the term in x2 [2 marks] 9 (a) (ii) Show that the first three terms in the binomial expans
- June 2024, Paper 3, Q1 (1 mark): Each of the series below shows the first four terms of a geometric series. Identify the only one of these geometric series that is convergent. [1 mark] Tick (✓)
- June 2023, Paper 1, Q14 (11 marks): (a) (i) Given that y = 2x write down dy dx [1 mark] 14 (a) (ii) Hence find ( 2x dx [2 marks] 14 (b) The area, A, bounded by the curve with equation y = 2x , the
- June 2022, Paper 1, Q12 (8 marks): (a) A geometric sequence has first term 1 and common ratio 1 2 12 (a) (i) Find the sum to infinity of the sequence. [2 marks] 12 (a) (ii) Hence, or otherwise, e
- November 2021, Paper 1, Q3 (1 mark): A geometric sequence has a sum to infinity of −3 A second sequence is formed by multiplying each term of the original sequence by −2 What is the sum to infinity
- November 2021, Paper 3, Q7 (10 marks): A building has a leaking roof and, while it is raining, water drips into a 12 litre bucket. When the rain stops, the bucket is one third full. Water continues t
- November 2020, Paper 3, Q8 (12 marks): The sum to infinity of a geometric series is 96 The first term of the series is less than 30 The second term of the series is 18 8 (a) Find the first term and c
- June 2019, Paper 1, Q16 (16 marks): (a) y = e−x( sinx + cos x) Find dy dx Simplify your answer. [3 marks] 16 (b) Hence, show that ( e−x sinx dx = ae−x( sinx + cos x) + c where a is a rational numb
- June 2018, Paper 3, Q9 (7 marks): Helen is creating a mosaic pattern by placing square tiles next to each other along a straight line. w The area of each tile is half the area of the previous ti
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