A robotic arm moves along a linear track. Its position pnp_npn (in cm) at step n n\,n is governed by the recurrence relation:
pn+1=3−(pn)2 p_{n+1} = 3 - (p_n)^2 pn+1=3−(pn)2In the case where the arm starts at p1=2p_1 = 2p1=2:
(i) Find the value of p3p_3p3.
(ii) Determine the value of p100p_{100}p100.
State a different value for p1p_1p1, other than p1=2p_1 = 2p1=2, which gives the same value for p100p_{100}p100 as found in part (a)(ii).
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.