plumiSequences and series: Edexcel A‑Level Maths questions
Every Edexcel A-Level Maths exam question on P.4 Sequences and series, 2019–2025, with its mark scheme and examiner’s report.
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![June 2022 Pure 1, question 13: (i) In an arithmetic series, the first term is a and the common difference is d. Show that Sn = n 2 [2a + (n − 1)d] (3) (ii) James saves money over a number of](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/9ma0-01-jun22-13-qp.webp)
All 32 questions on Sequences and series, as a list
- June 2025, Pure 1, Q3 (5 marks): The first three terms of an arithmetic sequence are 6k, 10 and 2k where k is a constant. (a) Find the value of k. (2) (b) Hence find the value of the sum of the
- June 2025, AS Pure, Q14 (7 marks): In this question you must show detailed reasoning. f (x) = (1 + kx) 8 where k is a constant. Given that the first 3 terms, in ascending powers of x, of the bino
- June 2024, Pure 1, Q2 (4 marks): (a) Find, in ascending powers of x, the first four terms of the binomial expansion of 1 9 1 2 x giving each term in simplest form. (3) (b) Give a reason why x =
- June 2024, Pure 1, Q9 (6 marks): The first 3 terms of a geometric sequence are 3 9 3 4 5 7 2 2 1 k k k where k is a constant. (a) Using algebra and making your reasoning clear, prove that k = 5
- June 2024, Pure 2, Q2 (5 marks): Jamie takes out an interest‑free loan of £8100 Jamie makes a payment every month to pay back the loan. Jamie repays £400 in month 1, £390 in month 2, £380 in mo
- June 2024, Pure 2, Q4 (5 marks): A sequence u1, u2, u3, ... is defined by u ku u n n 1 1 5 6 where k is a positive constant. Given that u3 = –1 (a) show that 6 5 4 0 2 k k (2) (b) Hence (i) fin
- June 2024, AS Pure, Q6 (6 marks): The binomial expansion of (1 + ax) 12 up to and including the term in x 2 is 1 – 15 2 x + kx 2 where a and k are constants. (a) Show that a = – 5 8 (2) (b) Henc
- June 2023, Pure 1, Q9 (7 marks): The first three terms of a geometric sequence are 3k + 4 12 – 3k k + 16 where k is a constant. (a) Show that k satisfies the equation 3k 2 – 62k + 40 = 0 (2) Gi
- June 2023, Pure 2, Q2 (6 marks): A sequence u1, u2, u3 ... is defined by u1 = 35 1 = 7cos 5( 1) 2 n n n nπ u u + + − − (a) (i) Show that u2 = 40 (ii) Find the value of u3 and the va
- June 2023, Pure 2, Q8 (6 marks): (a) Express 2 cos θ + 8 sin θ in the form R cos(θ – α) , where R and α are constants, R > 0 and 0 < α < 2 π Give the exact value of R and give the value of α in
- June 2023, Pure 2, Q13 (13 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (a) Find the first three term
- June 2023, AS Pure, Q14 (5 marks): Find, in simplest form, the coefficient of x5 in the expansion of (5)
- June 2022, Pure 1, Q13 (7 marks): (i) In an arithmetic series, the first term is a and the common difference is d. Show that Sn = n 2 [2a + (n − 1)d] (3) (ii) James saves money over a number of
- June 2022, Pure 2, Q3 (4 marks): A sequence of terms a1, a2, a3, … is defined by a1 = 3 an+1 = 8 − an (a) (i) Show that this sequence is periodic. (ii) State the order of this periodic sequence
- June 2022, Pure 2, Q7 (5 marks): (a) Find the first four terms, in ascending powers of x, of the binomial expansion of 4 9 − x writing each term in simplest form. (4) A student uses this expans
- June 2022, Pure 2, Q15 (10 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. Given that the first three terms of a
- June 2022, AS Pure, Q6 (6 marks): (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of 3 2 9 8 − x giving each term in simplest form. (4) f ( ) x x x x =
- November 2021, Pure 1, Q3 (6 marks): The sequence u1, u2, u3, … is defined by un + 1 = k − 24 un u1 = 2 where k is an integer. Given that u1 + 2u2 + u3 = 0 (a) show that 3k 2 − 58k + 240 = 0 (3) (b
- November 2021, Pure 1, Q5 (6 marks): In this question you should show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A company made a profit of
- November 2021, Pure 1, Q9 (11 marks): f(x) = 50 38 9 5 2 1 2 2 2 x x x x + + + ( ) − ( ) x ≠ −2 5 x ≠ 1 2 Given that f(x) can be expressed in the form A x B x C x 5 2 5 2 1 2 2 + + + ( ) + − where A
- November 2021, Pure 2, Q1 (4 marks): In an arithmetic series • the first term is 16 • the 21st term is 24 (a) Find the common difference of the series. (2) (b) Hence find the sum of the first 500 t
- November 2021, Pure 2, Q9 (3 marks): Show that ∑ ∞ 3 4 180 9 28 ( ) = n n cos (3) n = 2
- November 2021, AS Pure, Q8 (7 marks): g(x) = (2 + ax) 8 where a is a constant Given that one of the terms in the binomial expansion of g(x) is 3402x 5 (a) find the value of a. (4) Using this value o
- November 2020, Pure 1, Q1 (5 marks): (a) Find the first four terms, in ascending powers of x, of the binomial expansion of 1 8 1 2 + ( ) x giving each term in simplest form. (3) (b) Explain how you
- November 2020, Pure 1, Q5 (6 marks): A car has six forward gears. The fastest speed of the car ● in 1st gear is 28 km h–1 ● in 6th gear is 115 km h–1 Given that the fastest speed of the car in succ
- November 2020, Pure 1, Q13 (7 marks): A sequence of numbers a1, a2, a3, … is defined by an+1 = k a a n n + ( ) 2 n where k is a constant. Given that ● the sequence is a periodic sequence of orde
- November 2020, Pure 2, Q15 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A geometric series has common
- November 2020, AS Pure, Q6 (6 marks): (a) Find the first 4 terms, in ascending powers of x, in the binomial expansion of (1 + kx)10 where k is a non-zero constant. Write each coefficient as simply a
- June 2019, Pure 1, Q4 (6 marks): (a) Find the first three terms, in ascending powers of x, of the binomial expansion of 1 4 −x giving each coefficient in its simplest form. (4) The expansion ca
- June 2019, Pure 1, Q11 (7 marks): A competitor is running a 20 kilometre race. She runs each of the first 4 kilometres at a steady pace of 6 minutes per kilometre. After the first 4 kilometres,
- June 2019, Pure 2, Q8 (6 marks): (i) Find the value of 20 1 2 4 × ⎛ ⎝⎜ ⎞ ⎠⎟ = ∞ ∑ r r (3) (ii) Show that log5 1 48 2 1 2 n n n + + ⎛ ⎝⎜ ⎞ ⎠⎟= =∑ (3)
- June 2019, AS Pure, Q8 (5 marks): (a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of 2 3 4 6 + ⎛ ⎝⎜ ⎞ ⎠⎟ x giving each term in its simplest form. (4) (b) Explain
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