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≥1 P_{n+1} = 2(P_n - 3)^2 - 4, \quad n \ge 1 Pn+1=2(Pn−3)2−4,n≥1where 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 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.
