Question

Which sequence is modeled by the graph below? Points: (2,8) (3,4) (4,2) (5,1)

Answer 1

Answer:

$a_n=16 \cdot (\frac{1}{2})^{n-1}$

Step-by-step explanation:

This sequence is geometric because while x is going up by 1, the y sequence has a common ratio.

That is, term/previous equals same number per consecutive y terms.

So 1/2=2/4=4/8 is the common ratio.

The first term is when x=1. We can find this y by figuring out what we can multiply to our common ratio, 1/2, to get the next term,8.

Since 8(2)=16, then the first term is 16.

In general,

$y=a_1 \cdot (r)^{x-1}$

Or if preferred:

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

where $a_1$ is first term and $r$ is common ratio.

Plug in information:

$a_n=16 \cdot (\frac{1}{2})^{n-1}$