Question

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

Answer 1

Solution:

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;

$\begin{gathered} r=\frac{-39}{13}=\frac{117}{-39} \\ r=-3 \end{gathered}$

The first term is;

$a_1=13$

Therefore, the recursive formula is;

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