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 A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.