Question

What sequence is modeled by the graph below?

Answer 1

ANSWER

$a_n= \frac{1}{2}( {2}^{n - 1} )$

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.

$a_1= \frac{1}{2}$

The common ratio is

$r = \frac{2}{1} = 2$

The nth term is given by

$a_n=a_1 {(r}^{n - 1} )$

Let's substitute the values to get,

$a_n= \frac{1}{2} \times {(2}^{n - 1} )$

This simplifies to,

$a_n= \frac{1}{2} {(2}^{n - 1} )$