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.
200 exam-style questions on CCEA A Level Maths 3.3 Sequences and series (A-level only), covering 3.3.1 Sequences and series (A-level only), 3.3.2 Sequences and series (A-level only), 3.3.3 Sequences and series (A-level only), 3.3.4 Sequences and series (A-level only), 3.3.5 Sequences and series (A-level only), 3.3.6 Sequences and series (A-level only), 3.3.7 Sequences and series (A-level only), and 3.3.8 Sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.