plumiSecond order recurrence relations: OCR A‑Level Further Maths questions
OCR A-Level Further Maths past-paper questions on 9.2 Second 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.
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All 10 questions on Second order recurrence relations, as a list
- June 2025, Additional Pure Mathematics, Q8 (16 marks): (a) The members of the family of the sequences { Gn satisfy the first-order recurrence relation } G 1 25 . qG , for n 0 , 1 = - H n n + where q is a positive co
- June 2024, AS Additional Pure Mathematics, Q4 (5 marks): " ,, where n 4 The first five terms of the Fibonacci sequence, Fn H , are 1 F 1 , F 1 , F 2 , F = and F 3 5 = . 5 = = = 1 2 3 4 (a) Use the recurrence definitio
- June 2023, Additional Pure Mathematics, Q7 (10 marks): ^ h for n 1 a n n 7 Binet’s formula for the nth Fibonacci number is given by Fn 0 , where a = - b H 5 2 - - and b (with 0 b) are the roots of x x 1 0 . 2 2 a =
- June 2022, Additional Pure Mathematics, Q3 (6 marks): ^ h plays a significant role in the sequence of Fibonacci 1 3 The irrational number 1 5 z = + 2 numbers given by F 0 , F 1 = and 1 F F F - for n H . 1 0 = = + n
- June 2022, Additional Pure Mathematics, Q6 (12 marks): In a national park, the number of adults of a given species is carefully monitored and controlled. The number of adults, n months after the start of this projec
- June 2022, AS Additional Pure Mathematics, Q3 (7 marks): The sequence { Un is given by U } 0 , U 2 =- and U 1 U U n 1 for n H . 1 1 = = + + - n 2 n 1 n + + (a) List the first seven terms of this sequence. [2] The Fibo
- November 2021, Additional Pure Mathematics, Q8 (12 marks): (a) Solve the second-order recurrence system H 5 H 4 H with H 0 = , H 3 7 for = - 1 = n n n 2 1 + + n 0 . [5] H (b) (i) Write down the quadratic residues modulo
- November 2021, AS Additional Pure Mathematics, Q3 (6 marks): For positive integers n, the sequence of Fibonacci numbers, { Fn , starts with the terms } F 1 = , F 1 2 = , F 1 2 , … and is given by the recurrence relation F
- June 2019, Additional Pure Mathematics, Q1 (4 marks): u " , is defined by u + n 1 1 The sequence un 2 , u 1 = and u 5 - for n 2 . 0 = = H u n n 2 - Prove that the sequence is periodic with period 5. [4]
- June 2019, Additional Pure Mathematics, Q4 (10 marks): (a) Solve the second-order recurrence relation T 2 T 87 given that T 27 2 + =- 0 =- n n + and T 27 . [8] 1 = (b) Determine the value of T20. [2]
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