Sequences and Series

A sequence $a_1, a_2, a_3, \dots\,$ is defined by

\begin{aligned}a_1 &= q \\a_n &= 5a_{n-1} + 3, \quad n \geq 2\end{aligned}

a.

Find an expression for $a_2\,$ in terms of $q$ .

[1]

b.

Show that $a_3 = 25q + 18$ .

[2]

c.

Find $∑r=14ar\sum_{r=1}^4 a_r$ in terms of $q$ .

[3]

A sequence $a_1, a_2, a_3, \dots\,$ is defined by

\begin{aligned}a_1 &= q \\a_n &= 5a_{n-1} + 3, \quad n \geq 2\end{aligned}

a.

Find an expression for $a_2\,$ in terms of $q$ .

[1]

b.

Show that $a_3 = 25q + 18$ .

[2]

c.

Find $∑r=14ar\sum_{r=1}^4 a_r$ in terms of $q$ .

[3]

Sequences and Series Questions