November 2025 (9709/12). Question 2
Find the term independent of x in the expansion of 
November 2025 (9709/12). Question 8
The first three terms of a geometric progression are a, b and c respectively, where a, b and c are positive constants. The first three terms of an arithmetic progression are a, b and -3c respectively.
(a) Show that a2 – 10ac + 9c2 = 0 [3 marks]
It is now given that a = 9 and c takes the smaller of its two possible values.
(b) (i) Find the sum to infinity of the geometric progression. [5 marks]
(b) (ii) Find the sum of the first 20 terms of the arithmetic progression. [3 marks]
9709/11/M/J/25q3 – Mark Scheme
The third term of a geometric progression is 18 and the sum of the first three terms is 26. It is given that the common ratio is negative.
(a) Find the tenth term of the progression. Give your answer correct to 3 significant figures. [5 marks]
(b) Find the exact value of the sum to infinity of the progression. [2 marks]
9709/11/M/J/25q5 – Mark Scheme
(a) Find the first three terms, in ascending powers of x, in the expansion of each of the following expressions.
(i) (2 – px)5 [2 marks]
(ii) 
(b) Given that the coefficient of x2 in the expansion of 
9709/12/M/J/25q3
The coefficient of x7 in the expansion of 
Find the value of the constant p. [4 marks]
Maths with David 