plumiSeries: Edexcel International GCSE Further Maths questions
Edexcel International GCSE Further Maths past-paper questions on 5 Series, 2019–2025, with mark schemes and examiner’s reports where available.
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All 40 questions on Series, as a list
- June 2025 (R), Paper 1, Q2 (7 marks): An arithmetic series F has third term 8 and fifth term 20 Given that the sum to n terms of F is greater than 220 find the least value of n (7)
- June 2025 (R), Paper 2, Q4 (11 marks): 17 k 1 4 (i) Find the value of 3 2 (4) k 6 (ii) The common ratio of a geometric series G is positive. The third term of G is 7 and the ninth term of G is 448 13
- June 2025, Paper 2, Q4 (6 marks): A geometric series G has first term a and common ratio r The third term of G is 10 and the seventh term of G is 40 Given that the second term of G is negative,
- November 2024, Paper 1, Q2 (13 marks): The sum of the fifth, sixth and seventh terms of an arithmetic series A is nine times the sum of the first and second terms. The third term of A is 12 (a) Find
- June 2024 (R), Paper 1, Q5 (11 marks): The sum of the first 10 terms of an arithmetic series A is 36 k + where k is a constant. 1 The 6th term of A is 4 k + 1 (a) (i) Find an expression in terms of k
- June 2024 (R), Paper 2, Q8 (14 marks): The sum of the first 2 terms of a geometric series G is 360 The sum of the 2nd and 3rd terms of G is 288 The nth term of G is Un n 1 4 (a) Show that U A where A
- June 2024, Paper 1, Q3 (8 marks): n n 3 (a) Show that r n 5 3 2 5 1 (3) r 1 60 (b) Hence, or otherwise, evaluate r 5 3 (2) r 31 n Given that r 5 3 3783 r 1 (c) find the value of n (3)
- June 2024, Paper 1, Q8 (12 marks): The sum of the first and second terms of a geometric series G is 400 The sum of the second and third terms of G is 100 (a) Show that the common ratio of G is 1
- November 2023, Paper 1, Q7 (9 marks): A geometric series G with common ratio r, has first term 16 and third term 2704 625 (a) Find the two possible values of r (2) Given that r > 0 (b) find the sum
- November 2023, Paper 2, Q8 (10 marks): The sum to n terms of an arithmetic series A is Sn The sum of the first four terms of A is 42 and the fifth term of A is 23 n (a) Show that S Pr Q where P and Q
- June 2023 (R), Paper 1, Q8 (10 marks): The nth term of a geometric series G is Un and the sum of the first n terms of G is Sn n 25 3 Given that Un 4 5 (a) find the exact value of U5 (1) r 1 n A 3 (b)
- June 2023, Paper 1, Q1 (5 marks): n n r n 1 (a) Show that 3 2 2 3 7 r 1 (3) 40 r (b) Hence, or otherwise, evaluate 3 2 r 10 (2)
- June 2023, Paper 2, Q2 (6 marks): The nth term of a convergent geometric series is 8(1–2n) Find the sum to infinity of the series. Give your answer in the form p q where p and q are integers to
- January 2023 (R), Paper 1, Q3 (4 marks): An arithmetic series has first term 16 and common difference –5 The sum to n terms of this series is Sn Given that Sn < –450 find the least value of n (4)
- January 2023 (R), Paper 2, Q9 (12 marks): A geometric series G has common ratio r where r > 0 The third term of G is 27 2 and the sum of the first three terms of G is 57 2 Given that the sum to n terms
- January 2023, Paper 1, Q1 (4 marks): The nth term of an arithmetic series is an where a10 + a11 + a12 = 129 and a19 + a20 + a21 = 237 Find a1 (4)
- January 2023, Paper 2, Q6 (8 marks): The nth term of a geometric series G is Un The first three terms of G are given by U1 = q (4p + 1) U2 = q (2p + 3) U3 = q (2p – 3) (a) Find the possible values
- June 2022 (R), Paper 1, Q1 (5 marks): An arithmetic series has 5th term 16 and 100th term 301 Find the sum of the first 50 terms of the series. (5)
- June 2022 (R), Paper 2, Q3 (6 marks): A geometric series has first term a and common ratio r, where r > 0 Given that the 3rd term of the series is 5 and that the 5th term of the series is 5 2 (a) fi
- June 2022, Paper 1, Q4 (7 marks): The common ratio of a geometric series G is positive. The sum of the first 4 terms of G is 80 The sum to infinity of G is 81 Show that the sum of the first 7 te
- January 2022 (R), Paper 1, Q2 (8 marks): The nth term of an arithmetic series is un Given that u5 = 46 and that u20 = 181 (a) find (i) the common difference of this series, (ii) the first term of this
- January 2022 (R), Paper 2, Q5 (10 marks): A geometric series G has first term 12 and common ratio 3 8 (a) Find the sum to infinity of G (2) (b) Show that the 6th term of G can be written as 3 6 2 13 (3)
- January 2022, Paper 1, Q3 (7 marks): A geometric series G has first term a and common ratio r The 2nd term of G is 5 16 and the 5th term of G is 135 1024 (a) Find (i) the value of r (ii) the value
- January 2022, Paper 2, Q6 (13 marks): The sum of the first n terms of an arithmetic series is Sn where Sn = n (3 + 2n) (a) Find the value of S20 (2) n =∑ Given that Sn = (Ar + B) r 1 (b) find the va
- November 2021, Paper 1, Q9 (11 marks): n (5r – 1) = n =∑ 9 (a) Show that 2 (3 + 5n) (3) r 1 20 r =∑ (b) Hence, or otherwise, evaluate (5r – 1) (3) 10 n =∑ The sum of the first n terms of an arithmeti
- November 2021, Paper 2, Q7 (10 marks): A geometric series G has first term a and common ratio r The sum of the first three terms of G is 61 6 The sum to infinity of G is 125 6 (a) (i) Show that r = 4
- June 2021, Paper 1, Q4 (5 marks): The nth term of an arithmetic series is un where un = (n + 1) ln 4 Given that the sum of the first n terms of the series is Sn show that Sn = ln 2(n2 + an) wher
- June 2021, Paper 2, Q5 (7 marks): The nth term of a geometric series with common ratio r is un Given that u2 + u4 = 212.5 and that u3 + u4 = 62.5 (a) find the two possible values of r. (5) Given
- November 2020 (R), Paper 1, Q3 (7 marks): The nth term of an arithmetic series is un such that un = ln a + (n − 1) ln b where a and b are positive integers. Given that u2 = ln 12 and that u5 = ln 768 fi
- November 2020 (R), Paper 2, Q1 (6 marks): The nth term of an arithmetic series A is an The nth term of a geometric series G is tn For these two series a1 = t1 a10 = t3 = 48 a10 = 4t2 Find (i) the common
- November 2020, Paper 1, Q6 (10 marks): An arithmetic series A has first term a and common difference d. The sum Sn of the first n terms of A is given by Sn = n(15 + 2n) (a) Find the value of a and th
- November 2020, Paper 2, Q5 (8 marks): n 1 =∑ 5 (a) Show that r + = n n + ( 3 5 ) ( 3 13 ) 2 (3) r 1 50 =∑ (b) Hence evaluate r + ( 3 5 ) (2) r 35 n =∑ Given that r + = ( 3 5 ) 385 r 1 (c) find the v
- November 2020, Paper 2, Q7 (12 marks): A geometric series has first term (x – 3), second term (x + 1) and third term (4x – 2). (a) Find the two possible values of x. (5) Given that x < 1, (b) show th
- January 2020 (R), Paper 1, Q7 (11 marks): An arithmetic series P has first term a, common difference d and nth term un Given that u5 = 4x + 6 and that u8 = 7x + 3 (a) (i) show that d = x – 1 (ii) find t
- January 2020 (R), Paper 2, Q7 (13 marks): The geometric series G has first term a, common ratio r and nth term un 2 x+ 1 Given that u4 = e x + 2 and that u7 = e 2 −1 (a) show that r = e 2 (3) (b) Hence
- January 2020, Paper 1, Q1 (9 marks): The nth term of an arithmetic series is tn and the common difference of the series is d. Given that t2 + t9 = 0 and that t4 + t6 + t10 = 14 (a) (i) show that d
- January 2020, Paper 2, Q7 (12 marks): The 7th term of a geometric series is 192 and the 8th term of this geometric series is 1152 (a) Find, as a fraction in its simplest form, the 4th term of this g
- June 2019 (R), Paper 1, Q6 (10 marks): n r n n =∑ 6 (a) Show that ( 4 − 3 ) = ( 2 − 1 ) r 1 (3) n r =∑ (b) Hence, or otherwise, find the least value of n such that ( 4 − 3 ) 1000 r 1 (3) Given that S
- June 2019 (R), Paper 2, Q7 (11 marks): The nth term of a geometric series G is un The first term of G is a and the common ratio of G is U, where U 0 Given that u3 = 4 and that u7 = 16 (a) (i) show th
- June 2019, Paper 2, Q7 (9 marks): The sum of the first n terms of an arithmetic series is An where n A =∑ ( r = + 4 5 ) n r 1 (a) For this arithmetic series, find (i) the first term, (ii) the co
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