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.
308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.