A sequence u1,u2,u3,… u_1, u_2, u_3, \dots\,u1,u2,u3,… is defined by
u1=4un+1=kun+2,n≥1 \begin{aligned}u_1 &= 4 \\u_{n+1} &= ku_n + 2, \quad n \geq 1\end{aligned} u1un+1=4=kun+2,n≥1Find an expression for u2 u_2\,u2 in terms of kkk.
Show that u3=4k2+2k+2u_3 = 4k^2 + 2k + 2u3=4k2+2k+2.
Given that u3=32u_3 = 32u3=32, find the possible values of kkk.
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.