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)2−10 x_{n+1} = 2(x_n + 2)^2 - 10 xn+1=2(xn+2)2−10 x1=k−2 x_1 = k - 2 x1=k−2where 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 AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
