plumiSequences and series: Edexcel International A Level Maths questions
Every Edexcel International A Level Maths exam question on P2.4 Sequences and series, 2019–2025, with its mark scheme and examiner’s report.
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All 53 questions on Sequences and series, as a list
- June 2025, AS Pure 2 (P2), Q1 (6 marks): (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of (1 – 4x) 7 giving each term in simplest form. In the series expansion of (5 +
- June 2025, AS Pure 2 (P2), Q7 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. (i) A geometric series begins
- June 2025 (A), AS Pure 2 (P2), Q2 (6 marks): A geometric series has first term a and common ratio r. Given that • the third term in the series is 64 • the sixth term in the series is –8 (a) show that r = –
- June 2025 (A), AS Pure 2 (P2), Q5 (7 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. The sequence u1, u2, u3, ... is define
- June 2025 (A), AS Pure 2 (P2), Q7 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The binomial expansion, in as
- January 2025, AS Pure 2 (P2), Q1 (4 marks): The arithmetic series S is given by S 2 5 8 11 254 Find (a) the number of terms in the series, (b) the sum of the series.
- January 2025, AS Pure 2 (P2), Q2 (5 marks): (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of (2 – 5x) 8 giving each term in simplest form. This expansion is to be used to
- January 2025, AS Pure 2 (P2), Q4 (6 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Given that, in a particular g
- October 2024, AS Pure 2 (P2), Q2 (7 marks): A sequence of numbers u1, u2, u3, ... is defined by u1 = 7 un+1 = (–1) n un + k where k is a constant. (a) Show that u5 = 7 Given that ur r 30 1 4 (b) find the
- October 2024, AS Pure 2 (P2), Q5 (7 marks): (a) Find, in terms of a, the first 3 terms, in ascending powers of x, of the binomial expansion of (2 + ax) 6 where a is a non‑zero constant. Give each term in
- October 2024, AS Pure 2 (P2), Q7 (6 marks): Jem pays money into a savings scheme, A, over a period of 300 months. Jem pays £20 into scheme A in month 1, £20.50 in month 2, £21 in month 3 and so on, so tha
- June 2024, AS Pure 2 (P2), Q1 (5 marks): (a) Find the first four terms, in ascending powers of x, of the binomial expansion of 1 1 6 9 x giving each term in simplest form. (b) Hence find the coeff
- June 2024, AS Pure 2 (P2), Q2 (7 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. In an arithmetic series, • th
- June 2024, AS Pure 2 (P2), Q10 (8 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The number of dormice and the
- June 2024 (R), AS Pure 2 (P2), Q1 (5 marks): The sequence u1 , u2 , u3 , … satisfies un + 2 = 3un + 1 – 2un Given that • u1 = 7 • u3 = 4 (a) find the value of u2 (b) find u r r r 2 1 4
- June 2024 (R), AS Pure 2 (P2), Q4 (7 marks): (a) Find the first 4 terms, in ascending powers of x , of the binomial expansion of 3 2 6 x giving each coefficient in simplest form. (b) Hence find the coeffic
- June 2024 (R), AS Pure 2 (P2), Q8 (13 marks): (i) (a) In an arithmetic series the first term is a and the common difference is d. Show that S n a n d n 2 2 1 (b) Hence find 900 + 892 + 884 + … + 500 (
- January 2024, AS Pure 2 (P2), Q2 (3 marks): Find the coefficient of the term in x 7 of the binomial expansion of 3 8 4 12 x giving your answer in simplest form.
- January 2024, AS Pure 2 (P2), Q5 (8 marks): (i) Find the value of 6 0 25 1 . r r (ii) A sequence u1, u2, u3,... is defined by u u u u n n n n 1 1 3 3 2 (a) Show that this sequence is periodic. (b) S
- January 2024, AS Pure 2 (P2), Q7 (9 marks): Wheat is grown on a farm. • In year 1, the farm produced 300 tonnes of wheat. • In year 12, the farm is predicted to produce 4 000 tonnes of wheat. Model A assu
- October 2023, AS Pure 2 (P2), Q2 (5 marks): A sequence u1 , u2 , u3 , … is defined by u1 = 3 un+1 = 2 – 4 un (a) Find the value of u2 , the value of u3 and the value of u4 (b) Find the value of ur r 1 100
- October 2023, AS Pure 2 (P2), Q8 (7 marks): In a large theatre there are n rows of seats, where n is a constant. The number of seats in the first row is a, where a is a constant. In each subsequent row th
- October 2023, AS Pure 2 (P2), Q10 (12 marks): (i) (a) Find, in ascending powers of x, the 2nd, 3rd and 5th terms of the binomial expansion of (3 + 2x) 6 For a particular value of x, these three terms form c
- June 2023, AS Pure 2 (P2), Q4 (7 marks): The binomial expansion, in ascending powers of x, of (3 + px) 5 where p is a constant, can be written in the form A + Bx + Cx 2 + Dx 3 ... where A, B, C and D a
- June 2023, AS Pure 2 (P2), Q6 (9 marks): In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A software developer released
- June 2023, AS Pure 2 (P2), Q11 (8 marks): A sequence u1, u2, u3, ... is defined by un+1 = b – aun u1 = 3 where a and b are constants. (a) Find, in terms of a and b, (i) u2 (ii) u3 Given • un n 153 1 3 •
- January 2023, AS Pure 2 (P2), Q3 (7 marks): f x kx ( ) = + 2 8 7 where k is a non‑zero constant (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of f (x). Give eac
- January 2023, AS Pure 2 (P2), Q7 (7 marks): A geometric sequence has first term a and common ratio r, where r > 0 Given that • the 3rd term is 20 • the 5th term is 12.8 (a) show that r = 0.8 (b) Hence fin
- October 2022, AS Pure 2 (P2), Q2 (7 marks): A curve C has equation y = f(x) where f(x) = (2 – kx)5 and k is a constant. Given that when f(x) is divided by (4x – 5) the remainder is 243 32 (a) show that k
- October 2022, AS Pure 2 (P2), Q3 (7 marks): A sequence a1, a2, a3, … is defined by an = cos2 3 nπ Find the exact values of (a) (i) a1 (ii) a2 (iii) a3 (b) Hence find the exact value of 50 2 1
- October 2022, AS Pure 2 (P2), Q8 (7 marks): A geometric sequence has first term a and common ratio r Given that S∞ = 3a (a) show that r = 2 3 Given also that u2 – u4 = 16 where uk is the kth term of this
- June 2022, AS Pure 2 (P2), Q1 (4 marks): Find the first four terms, in ascending powers of x, of the binomial expansion of 2 3 8 10 + x Give each coefficient as an integer.
- June 2022, AS Pure 2 (P2), Q6 (8 marks): In a geometric sequence u1 , u2 , u3 , … • the common ratio is r • u2 + u3 = 6 • u4 = 8 (a) Show that r satisfies 3r2 − 4r − 4 = 0 Given that the geometric sequ
- January 2022, AS Pure 2 (P2), Q3 (7 marks): (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of 2 4 8 − kx where k is a non‑zero constant. Give each term in simple
- January 2022, AS Pure 2 (P2), Q8 (9 marks): A metal post is repeatedly hit in order to drive it into the ground. Given that • on the 1st hit, the post is driven 100 mm into the ground • on the 2nd hit, th
- October 2021, AS Pure 2 (P2), Q1 (6 marks): The first three terms, in ascending powers of x, of the binomial expansion of (1 + kx) 16 are 1, −4x and px2 where k and p are constants. (a) Find, in simplest
- October 2021, AS Pure 2 (P2), Q2 (5 marks): A sequence is defined by u1 = 6 un+1 = kun + 3 where k is a positive constant. (a) Find, in terms of k, an expression for u3 Given that un n=∑ 1 3 = 117 (b) fin
- October 2021, AS Pure 2 (P2), Q5 (6 marks): A company that owned a silver mine • extracted 480 tonnes of silver from the mine in year 1 • extracted 465 tonnes of silver from the mine in year 2 • extracted
- October 2021, AS Pure 2 (P2), Q7 (10 marks): (i) A geometric sequence has first term 4 and common ratio 6 Given that the nth term is greater than 10 100, find the minimum possible value of n. (ii) A differ
- June 2021, AS Pure 2 (P2), Q1 (7 marks): Adina is saving money to buy a new computer. She saves £5 in week 1, £5.25 in week 2, £5.50 in week 3 and so on until she has enough money, in total, to buy the
- June 2021, AS Pure 2 (P2), Q4 (8 marks): (a) Find, in ascending powers of x, up to and including the term in x3, the binomial expansion of 2 8 13 + x fully simplifying each coefficient. (b) U
- January 2021, AS Pure 2 (P2), Q4 (8 marks): (a) Find the first three terms, in ascending powers of x, of the binomial expansion of 2 6 + ( ) px where p is a constant. Give each term in simplest form. Give
- January 2021, AS Pure 2 (P2), Q8 (7 marks): A sequence a1 , a2 , a3 , … is defined by an + 1 = 2(an + 3) 2 − 7 a1 = p − 3 where p is a constant. (a) Find an expression for a2 in terms of p, giving your an
- January 2021, AS Pure 2 (P2), Q10 (11 marks): In this question you must show detailed reasoning. Owen wants to train for 12 weeks in preparation for running a marathon. During the 12-week period he will run
- October 2020, AS Pure 2 (P2), Q1 (7 marks): (a) Find the first 4 terms, in ascending powers of x, of the binomial expansion of 2 4 10 − x giving each term in its simplest form. (b) Hence find th
- October 2020, AS Pure 2 (P2), Q5 (11 marks): Ben is saving for the deposit for a house over a period of 60 months. Ben saves £100 in the first month and in each subsequent month, he saves £5 more than the
- October 2020, AS Pure 2 (P2), Q8 (8 marks): A geometric series has first term a and common ratio r. (a) Prove that the sum of the first n terms of this series is given by Sn = a r r n ( ) 1 1 − − The seco
- January 2020, AS Pure 2 (P2), Q2 (7 marks): One of the terms in the binomial expansion of (3 + ax)6, where a is a constant, is 540x4 (a) Find the possible values of a. (b) Hence find the term independent
- January 2020, AS Pure 2 (P2), Q5 (8 marks): In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A colony of bees is being studied. The
- January 2020, AS Pure 2 (P2), Q8 (7 marks): (i) An arithmetic series has first term a and common difference d. Prove that the sum to n terms of this series is n a n d 2 2 1 + − ( ) { } (ii) A sequence u1,
- June 2019, AS Pure 2 (P2), Q1 (4 marks): A sequence a1, a2, a3, ... is defined by an + 1 = 4 – an a1 = 3 Find the value of (a) (i) a2 (ii) a107 (b) n=∑ 1 200 (2an – 1)
- June 2019, AS Pure 2 (P2), Q4 (7 marks): (a) Find the first four terms, in ascending powers of x, of the binomial expansion of 2 1 4 6 − ⎛ ⎝⎜ ⎞ ⎠⎟ x (b) Given that x is small, so terms in x4 and higher
- June 2019, AS Pure 2 (P2), Q7 (9 marks): Kim starts working for a company. Ɣ In year 1 her annual salary will be £16 200 Ɣ In year 10 her annual salary is predicted to be £31 500 Model A assumes that h
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