1.6.7 Generate a sequence by formula or recurrence (A-level only)

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

\begin{aligned}x_1 &= 5 \\x_{n+1} &= px_n - 6, \quad n \geq 1\end{aligned}

a.

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

[1]

b.

Show that $x_3 = 5p^2 - 6p - 6$ .

[2]

c.

Given that $x_3 = 21$ , find the possible values of $p$ .

[3]

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

\begin{aligned}x_1 &= 5 \\x_{n+1} &= px_n - 6, \quad n \geq 1\end{aligned}

a.

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

[1]

b.

Show that $x_3 = 5p^2 - 6p - 6$ .

[2]

c.

Given that $x_3 = 21$ , find the possible values of $p$ .

[3]

1.6.7 Generate a sequence by formula or recurrence (A-level only) Questions