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).
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only), matched to the AQA A Level Maths (7357) 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.
