The temperature TnT_nTn (in ∘C{^\circ}\text{C}∘C) inside a specialized climate-controlled incubator on day n n\,n is modeled by the recurrence relation:
Tn+1=13−Tn2,n≥1T_{n+1} = 13 - T_n^2, \quad n \ge 1Tn+1=13−Tn2,n≥1
In the case where the initial temperature is set to T1=4T_1 = 4T1=4:
(i) Calculate the value of T3T_3T3.
(ii) Deduce the value of T100T_{100}T100.
State a different value for T1T_1T1, other than T1=4T_1 = 4T1=4, which would result in the same value for T100T_{100}T100 as found in part (a)(ii). Justify your answer.
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.