A sequence x1,x2,x3,… x_1, x_2, x_3, \dots\,x1,x2,x3,… is defined by
x1=2xn+1=axn−5,n≥1 \begin{aligned}x_1 &= 2 \\x_{n+1} &= ax_n - 5, \quad n \geq 1\end{aligned} x1xn+1=2=axn−5,n≥1Find an expression for x2 x_2\,x2 in terms of aaa.
Show that x3=2a2−5a−5x_3 = 2a^2 - 5a - 5x3=2a2−5a−5.
Given that x3=20x_3 = 20x3=20, find the possible values of aaa.
