A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=5xn+1=pxn−6,n≥1 \begin{aligned}x_1 &= 5 \\x_{n+1} &= px_n - 6, \quad n \geq 1\end{aligned} x1xn+1=5=pxn−6,n≥1Find an expression for x2 x_2\,x2 in terms of ppp.
Show that x3=5p2−6p−6x_3 = 5p^2 - 6p - 6x3=5p2−6p−6.
Given that x3=21x_3 = 21x3=21, find the possible values of ppp.
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.