A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=1xn+1=axn+6,n≥1 \begin{aligned}x_1 &= 1 \\x_{n+1} &= ax_n + 6, \quad n \geq 1\end{aligned} x1xn+1=1=axn+6,n≥1Find an expression for x2 x_2\,x2 in terms of aaa.
Show that x3=a2+6a+6x_3 = a^2 + 6a + 6x3=a2+6a+6.
Given that x3=22x_3 = 22x3=22, find the possible values of aaa.
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.
