1.7 D: Sequences and series

65%

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

\begin{aligned}x_1 &= k \\x_n &= 4x_{n-1} - 1, \quad n \geq 2\end{aligned}

a.

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

[1]

b.

Show that $x_3 = 16k - 5$ .

[2]

c.

Find $∑r=14xr\sum_{r=1}^4 x_r$ in terms of $k$ .

[3]

65%

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

\begin{aligned}x_1 &= k \\x_n &= 4x_{n-1} - 1, \quad n \geq 2\end{aligned}

a.

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

[1]

b.

Show that $x_3 = 16k - 5$ .

[2]

c.

Find $∑r=14xr\sum_{r=1}^4 x_r$ in terms of $k$ .

[3]

1.7 D: Sequences and series Questions