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

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,

Or if preferred:

where is first term and is common ratio.

Plug in information:

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0