Question

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

1.) 1/2
2.) 2
3.) 3
4.) 6

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`