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)2p_{n+1} = 3 - (p_n)^2pn+1=3−(pn)2
In 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 Edexcel A Level Maths 3.7 Recurrence Relations with exam-style questions for A Level Maths. 36 questions, matched to the Edexcel A Level Maths (9MA0) 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.