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).
200 exam-style questions on CCEA A Level Maths 3.3 Sequences and series (A-level only), covering 3.3.1 Sequences and series (A-level only), 3.3.2 Sequences and series (A-level only), 3.3.3 Sequences and series (A-level only), 3.3.4 Sequences and series (A-level only), 3.3.5 Sequences and series (A-level only), 3.3.6 Sequences and series (A-level only), 3.3.7 Sequences and series (A-level only), and 3.3.8 Sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.