A sequence of sensor measurements P1,P2,P3,…P_1, P_2, P_3, \dotsP1,P2,P3,… is defined by the recurrence relation
Pn+1=2(Pn−3)2−4,n≥1P_{n+1} = 2(P_n - 3)^2 - 4, \quad n \ge 1Pn+1=2(Pn−3)2−4,n≥1
where the first measurement is given by P1=k+3P_1 = k + 3P1=k+3 and kkk is a constant.
Find an expression for P2P_2P2 in terms of kkk, giving your answer in its simplest form.
Given that ∑n=13Pn=k+12\sum_{n=1}^{3} P_n = k + 12∑n=13Pn=k+12,
determine the possible values of P2P_2P2.
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.