First order recurrence relations: Edexcel A‑Level Further Maths questions

Edexcel A-Level Further Maths past-paper questions on 9.1 First order recurrence relations, 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.

All 17 questions on First order recurrence relations, as a list

June 2025, Decision 2, Q7 (14 marks): A sequence {un }, where n  0, satisfies the first order recurrence relation (*) un + 1 = αun – β(k n) (*) where α, β, k are non-zero constants and α ≠ k (a) De
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 2025, AS Decision 2, Q4 (9 marks): A sequence{ } un , where n 1, satisfies the recurrence relation 4 2 3 5 1 u u n n n Given that u1 2 (a) solve the recurrence relation, giving un in terms of n
June 2024, Decision 2, Q2 (3 marks): The general solution of the first order recurrence relation u au bn cn d n n 1 2 n  0 is given by u A n n n ( ) 3 5 1 2 where A is an arbitrary non‑zero consta
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, Decision 2, Q7 (8 marks): Martina decides to open a bank account to help her to save for a holiday. Each month she puts £k into the account and allows herself to spend one quarter of wha
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 2023, AS Decision 2, Q4 (8 marks): A sequence {un}, where n  0, satisfies the recurrence relation un + 1 = 3 2 un – 2n 2 – 4 u0 = k where k is an integer. (a) Determine an expression for un in t
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, Decision 2, Q8 (9 marks): The owner of a new company models the number of customers that the company will have at the end of each month. The owner assumes that • a constant proportion, p
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
June 2022, AS Decision 2, Q4 (10 marks): A sequence {un}, where n  0, satisfies the recurrence relation un + 1 + 3un = n + k where k is a non‑zero constant. Given that u0 = 1 (a) solve the recurrence
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
November 2020, AS Decision 2, Q4 (8 marks): A sequence {un}, where n 1, satisfies the recurrence relation 2un = un – 1 – kn2 where 4u2 – u0 = 27k2 and k is a non‑zero constant. Show that, as n becomes la
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 2019, AS Decision 2, Q2 (6 marks): (a) Find the general solution of the recurrence relation un + 1 = 3un + 2n n . 1 (4) (b) Find the particular solution of this recurrence relation for which u1 =
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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