Question

What is the recursive formula for finding the nth term of the given geometric sequence?13,-39,117,-351,...

Answer 1

Given:

`13,-39,117,-351,...`

The recursive formula of a geometric sequence is given by;

`a_n=a_(n-1)\cdot r`

The common ratio is;

`\begin{gathered} r=(-39)/(13)=(117)/(-39) \\ r=-3 \end{gathered}`

The first term is;

`a_1=13`

Therefore, the recursive formula is;

`\begin{gathered} a_n=a_(n-1)(-3) \\ a_n=-3(a_(n-1)) \end{gathered}`