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

Question

asked Feb 22, 2020 182k views

2 Answers

Winton Hou · Answer 1 · 2020-02-29T04:51:00+0000

Answer:

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

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
is common ratio.

Plug in information:

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