plumiFurther sequences and series: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on FP.9 Further sequences and series, 2018–2025, with its mark scheme and examiner’s report.
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All 16 questions on Further sequences and series, as a list
- June 2025, Further Pure 2, Q4 (9 marks): A sequence is defined by un+2 = 6un+1 – 8un n 1 u1 = 399.6 u2 = 798.4 (a) Prove by induction that, for n ∈ un = 200(2 n) – 1 10 (4 n) (6) (b) Hence determin
- June 2025, AS Further Pure 2, Q3 (10 marks): A loan of £180 000 is taken out to buy a house. The monthly interest rate on the loan is 0.15% The interest is added to the balance of the loan at the end of ea
- June 2024, Further Pure 2, Q2 (5 marks): Determine a closed form for the recurrence system u n u u u u n n n 1 2 2 1 4 6 6 9 1 2 3 ( , , , ) (5)
- June 2024, AS Further Pure 2, Q5 (9 marks): Figure 1 Figure 1 shows the first three stages of a pattern that is created by a recursive process. The process starts with a square and proceeds as follows • e
- June 2023, Further Pure 2, Q3 (9 marks): In a model for the number of subscribers to a new social media channel it is assumed that • each week 20% of the subscribers at the start of the week cancel the
- June 2023, Further Pure 2, Q6 (7 marks): Determine a closed form for the recurrence relation u u u u u n n n n n 0 1 2 1 1 0 4 2 4 3 (7)
- June 2023, AS Further Pure 2, Q4 (9 marks): A student takes out a loan for £1000 from a bank. The bank charges 0.5% monthly interest on the amount of the loan yet to be repaid. At the end of each month •
- June 2022, Further Pure 2, Q3 (8 marks): A B C Figure 1 There are three lily pads on a pond. A frog hops repeatedly from one lily pad to another. The frog starts on lily pad A, as shown in Figure 1. In
- June 2022, Further Pure 2, Q6 (6 marks): (a) Determine the general solution of the recurrence relation u n = 2u n – 1 – u n – 2 + 2n n 2 (4) (b) Hence solve this recurrence relation given that u0 = 2
- June 2022, AS Further Pure 2, Q5 (9 marks): A person takes a course of a particular vitamin. Before the course there was none of the vitamin in the person’s body. During the course, vitamin tablets are ta
- November 2021, Further Pure 2, Q6 (6 marks): A recurrence system is defined by un+2 = 9(n + 1) 2 un − 3un+1 n 1 u1 = −3, u2 = 18 Prove by induction that, for n ∈ , un = (−3) n n! (6)
- November 2020, Further Pure 2, Q2 (9 marks): Solve the recurrence system u1 = 1 u2 = 4 9un + 2 – 12un + 1 + 4un = 3n (9)
- November 2020, AS Further Pure 2, Q4 (10 marks): Sam borrows £10 000 from a bank to pay for an extension to his house. The bank charges 5% annual interest on the portion of the loan yet to be repaid. Immediate
- June 2019, Further Pure 2, Q3 (8 marks): The number of visits to a website, in any particular month, is modelled as the number of visits received in the previous month plus k times the number of visits
- June 2019, AS Further Pure 2, Q5 (11 marks): On Jim’s 11th birthday his parents invest £1000 for him in a savings account. The account earns 2% interest each year. On each subsequent birthday, Jim’s parent
- June 2018, AS Further Pure 2, Q3 (10 marks): 3 A tree at the bottom of a garden needs to be reduced in height. The tree is known to increase in height by 15 centimetres each year. On the first day of every
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