plumiSequences and series: WJEC A‑Level Maths questions
Every WJEC A-Level Maths exam question on P.4 Sequences and series, 2018–2025, with its mark scheme and examiner’s report.
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![Summer 2025 Unit 3, question 7: 7. The first and last terms of an arithmetic series are –3 and 61 respectively. The sum of all of the terms is 957. Determine (a) the number of terms, [2] (b) t](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun25-07-qp.webp)
![Summer 2025 Unit 3, question 12: x in ascending powers of x up to and including the term in x3. 12. Expand 3 1 2 x State the range of values of x for which the expansion is valid. [7]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun25-12-qp.webp)
![Summer 2024 Unit 3, question 7: 7. Showing all your working, evaluate 50 4 r 5 (a) , [4] r 3](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun24-07-qp.webp)
![Summer 2024 AS Unit 1, question 9: (2 x ) up to and including the term in x2. 9. (a) Write down the binomial expansion of [3] (b) Given that 6 2 (1 ax )(2 x ) 64 bx 336 x , find th](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun24-09-qp.webp)
![Summer 2023 Unit 3, question 1: 1 The 12th term of an arithmetic series is 41 and the sum of the first 16 terms is 488. Find the first term and the common difference of the series. [5]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun23-01-qp.webp)
![Summer 2023 Unit 3, question 3: 0 3 a) Express )2 in terms of partial fractions. [4] ( ) 1+ 2x ( 1− x 9 b) Using your answer from part (a), find the expansion of )2 in ( ) 1+ 2x ( 1− x ascendi](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun23-03-qp.webp)
![Summer 2023 AS Unit 1, question 1: 1 a) Using the binomial theorem, write down and simplify the first three terms in the expansion of (1 – 3x)9 in ascending powers of x. [3] Hence, by writing x =](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun23-01-qp.webp)
![Summer 2022 Unit 3, question 9: 9 For each of the following sequences, find the first 5 terms, u1 to u5. Describe the behaviour of each sequence. 2( ) un = sin nπ a) [2] u6 = 33, un = 2un−1 −1](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun22-09-qp.webp)
![Summer 2022 AS Unit 1, question 13: ( )5 2 − 3x 1 3 Find the term which is independent of x in the expansion of . [4] x3](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun22-13-qp.webp)
![Summer 2019 Unit 3, question 2: − x Expand in ascending powers of x up to and including the term in x3. State the 0 2 1+ 2x range of values of x for which the expansion is valid. [6]](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun19-02-qp.webp)
![Summer 2019 Unit 3, question 3: 3 The nth term of a number sequence is denoted by xn. The (n + 1)th term is defined by xn+1 = 4xn – 3 and x3 = 113. a) Find the values of x2 and x1. [2] b) Dete](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/1300u30-jun19-03-qp.webp)
![Summer 2019 AS Unit 1, question 12: 2 In the binomial expansion of (2 – 5x)8, find a) the number of terms, [1] the 4th term, when the expansion is in ascending powers of x, b) [2] c) the greatest](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/2300u10-jun19-12-qp.webp)
All 24 questions on Sequences and series, as a list
- Summer 2025, Unit 3, Q7 (5 marks): 7. The first and last terms of an arithmetic series are –3 and 61 respectively. The sum of all of the terms is 957. Determine (a) the number of terms, [2] (b) t
- Summer 2025, Unit 3, Q12 (7 marks): x in ascending powers of x up to and including the term in x3. 12. Expand 3 1 2 x State the range of values of x for which the expansion is valid. [7]
- Summer 2025, Unit 3, Q16 (6 marks): 16. A person borrows £50 000 which is to be repaid over 20 years in 20 equal annual amounts. The lender charges an annual compound interest rate of 5% which rem
- Summer 2025, AS Unit 1, Q16 (7 marks): 16. The binomial expansion of 7 2 2 x is given by 7 2 x 2 = a0 + a1x2 + a2x4 + a3x6 + a4x8 + a5x10 + a6x12 + a7x14. (a) Find the numerical values of
- Summer 2024, Unit 3, Q7 (7 marks): 7. Showing all your working, evaluate 50 4 r 5 (a) , [4] r 3
- Summer 2024, Unit 3, Q15 (5 marks): 15. Robert wants to deposit £P into a savings account. He has a choice of two accounts. • Account A offers an annual compound interest rate of 1%. • Account B o
- Summer 2024, AS Unit 1, Q9 (9 marks): (2 x ) up to and including the term in x2. 9. (a) Write down the binomial expansion of [3] (b) Given that 6 2 (1 ax )(2 x ) 64 bx 336 x , find th
- Summer 2023, Unit 3, Q1 (5 marks): 1 The 12th term of an arithmetic series is 41 and the sum of the first 16 terms is 488. Find the first term and the common difference of the series. [5]
- Summer 2023, Unit 3, Q3 (11 marks): 0 3 a) Express )2 in terms of partial fractions. [4] ( ) 1+ 2x ( 1− x 9 b) Using your answer from part (a), find the expansion of )2 in ( ) 1+ 2x ( 1− x ascendi
- Summer 2023, Unit 3, Q5 (6 marks): 5 A tree is 80 cm in height when it is planted. In the first year, the tree grows in height by 32 cm. In each subsequent year, the tree grows in height by 90% o
- Summer 2023, AS Unit 1, Q1 (6 marks): 1 a) Using the binomial theorem, write down and simplify the first three terms in the expansion of (1 – 3x)9 in ascending powers of x. [3] Hence, by writing x =
- Summer 2022, Unit 3, Q4 (6 marks): 4 The sum to infinity of a geometric series with first term a and common ratio r is 120. The sum to infinity of another geometric series with first term a and c
- Summer 2022, Unit 3, Q6 (5 marks): 6 Geraint opens a savings account. He deposits £10 in the first month. In each subsequent month, the amount he deposits is 20 pence greater than the amount he d
- Summer 2022, Unit 3, Q8 (8 marks): − x 0 8 Find the first three terms in the binomial expansion of in ascending powers 1+ 3x of x. State the range of values of x for which the expansion is valid.
- Summer 2022, Unit 3, Q9 (5 marks): 9 For each of the following sequences, find the first 5 terms, u1 to u5. Describe the behaviour of each sequence. 2( ) un = sin nπ a) [2] u6 = 33, un = 2un−1 −1
- Summer 2022, AS Unit 1, Q13 (4 marks): ( )5 2 − 3x 1 3 Find the term which is independent of x in the expansion of . [4] x3
- Summer 2019, Unit 3, Q2 (6 marks): − x Expand in ascending powers of x up to and including the term in x3. State the 0 2 1+ 2x range of values of x for which the expansion is valid. [6]
- Summer 2019, Unit 3, Q3 (4 marks): 3 The nth term of a number sequence is denoted by xn. The (n + 1)th term is defined by xn+1 = 4xn – 3 and x3 = 113. a) Find the values of x2 and x1. [2] b) Dete
- Summer 2019, Unit 3, Q8 (11 marks): 8 a) The 3rd, 19th and 67th terms of an arithmetic sequence form a geometric sequence. Given that the arithmetic sequence is increasing and that the first term
- Summer 2019, AS Unit 1, Q12 (6 marks): 2 In the binomial expansion of (2 – 5x)8, find a) the number of terms, [1] the 4th term, when the expansion is in ascending powers of x, b) [2] c) the greatest
- Summer 2018, Unit 3, Q6 (5 marks): −1 ( ) 1− 4x 0 6 Write down the first three terms in the binomial expansion of in ascending 2 powers of x. State the range of values of x for which the expansio
- Summer 2018, Unit 3, Q8 (5 marks): 8 Find seven numbers which are in arithmetic progression such that the last term is 71 and the sum of all of the numbers is 329. [5]
- Summer 2018, Unit 3, Q9 (10 marks): 9 a) Explain why the sum to infinity of a geometric series with common ratio r only converges when | r | < 1. [1] b) A geometric progression V has first term 2
- Summer 2018, AS Unit 1, Q10 (4 marks): ( ) 4 a + b 1 0 a) Use the binomial theorem to expand . [2] ( ) ( ) 4 4 a + b + a − b b) Hence, deduce an expression in terms of a and b for . [2]
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