Question

What is the common ratio, r, for the sequence represented by the formula a∨n= 3(2)ˆ-n

Answer 1

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio} \end{cases}\\\\ -------------------------------\\\\ a_n=3(2)^{-n}\implies a_n=3(2^{-1})n\implies a_n=3\left( \stackrel{r}{\cfrac{1}{2}} \right)^n$