Question

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

a. an = one half (16)n − 1
b. an = 4(2)n − 1
c. an = 16(−2)n − 1
d. an = 16( one half )n − 1

Answer 1

Explanation:

The answer is option d or an = 16( one half )n − 1

Answer 2

`a_n=16 \cdot ((1)/(2))^(n-1)`

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 ((1)/(2))^(n-1)`