1.4 Sequences and Series

A sequence $u_1, u_2, u_3, \dots\,$ is defined by

\begin{aligned}u_1 &= 4 \\u_{n+1} &= ku_n + 2, \quad n \geq 1\end{aligned}

a.

Find an expression for $u_2\,$ in terms of $k$ .

[1]

b.

Show that $u_3 = 4k^2 + 2k + 2$ .

[2]

c.

Given that $u_3 = 32$ , find the possible values of $k$ .

[3]

A sequence $u_1, u_2, u_3, \dots\,$ is defined by

\begin{aligned}u_1 &= 4 \\u_{n+1} &= ku_n + 2, \quad n \geq 1\end{aligned}

a.

Find an expression for $u_2\,$ in terms of $k$ .

[1]

b.

Show that $u_3 = 4k^2 + 2k + 2$ .

[2]

c.

Given that $u_3 = 32$ , find the possible values of $k$ .

[3]

1.4 Sequences and Series Questions