A sequence of daily depth changes in a reservoir, x1,x2,x3,…x_1, x_2, x_3, \dotsx1,x2,x3,…, is defined by the recurrence relation xn+1=2(xn+2)2−10x_{n+1} = 2(x_n + 2)^2 - 10xn+1=2(xn+2)2−10 x1=k−2x_1 = k - 2x1=k−2 where kkk is a constant.
Find an expression for x2x_2x2 in terms of kkk, giving your answer in simplest form.
Given that ∑n=13xn=k+22\sum_{n=1}^{3} x_n = k + 22∑n=13xn=k+22
find the possible values of x2x_2x2.
Practise Edexcel A Level Maths 3.7 Recurrence Relations with exam-style questions for A Level Maths. 36 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.