Sequences and Series

A sequence $x_1, x_2, x_3, \dots\,$ is defined by

\begin{aligned}x_1 &= 1 \\x_{n+1} &= ax_n + 6, \quad n \geq 1\end{aligned}

a.

Find an expression for $x_2\,$ in terms of $a$ .

[1]

b.

Show that $x_3 = a^2 + 6a + 6$ .

[2]

c.

Given that $x_3 = 22$ , find the possible values of $a$ .

[3]

A sequence $x_1, x_2, x_3, \dots\,$ is defined by

\begin{aligned}x_1 &= 1 \\x_{n+1} &= ax_n + 6, \quad n \geq 1\end{aligned}

a.

Find an expression for $x_2\,$ in terms of $a$ .

[1]

b.

Show that $x_3 = a^2 + 6a + 6$ .

[2]

c.

Given that $x_3 = 22$ , find the possible values of $a$ .

[3]

Sequences and Series Questions