Given that the series is 1, 3, 9, 27, ............
The common ratio will be
[tex]Common\text{ ratio=}\frac{2nd\text{ term}}{1st\text{ term}}=\frac{3}{1}=3[/tex]
So the common ratio is 3.
The explicit formula uses starting term and the recursive formula uses the previous term.
As
[tex]\begin{gathered} Explicit\text{ form} \\ a_n=3^{n-1} \\ Recursive\text{ form} \\ a_n=a_{n-1}\times3 \end{gathered}[/tex]
These are the required forms.
