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 Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 156 questions covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series, 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.
