A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=4xn+1=axn−3,n≥1 \begin{aligned}x_1 &= 4 \\x_{n+1} &= ax_n - 3, \quad n \geq 1\end{aligned} x1xn+1=4=axn−3,n≥1Find an expression for x2 x_2\,x2 in terms of aaa.
Show that x3=4a2−3a−3x_3 = 4a^2 - 3a - 3x3=4a2−3a−3.
Given that x3=7x_3 = 7x3=7, find the possible values of aaa.
