ANSWER
[tex]a_n= \frac{1}{2}( {2}^{n - 1} )[/tex]
EXPLANATION
The corresponding ordered pairs from the graph are:
(2,1) (3,2) (4,4) (5,8)
The y-values are:
1,2,4,8
The first term term is the term before 1,this has to be.
[tex]a_1= \frac{1}{2} [/tex]
The common ratio is
[tex]r = \frac{2}{1} = 2[/tex]
The nth term is given by
[tex]a_n=a_1 {(r}^{n - 1} )[/tex]
Let's substitute the values to get,
[tex]a_n= \frac{1}{2} \times {(2}^{n - 1} )[/tex]
This simplifies to,
[tex]a_n= \frac{1}{2} {(2}^{n - 1} )[/tex]
