A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=3xn+1=axn−4,n≥1 \begin{aligned}x_1 &= 3 \\x_{n+1} &= ax_n - 4, \quad n \geq 1\end{aligned} x1xn+1=3=axn−4,n≥1Find an expression for x2 x_2\,x2 in terms of aaa.
Show that x3=3a2−4a−4x_3 = 3a^2 - 4a - 4x3=3a2−4a−4.
Given that x3=11x_3 = 11x3=11, find the possible values of aaa.
