Which sequence is modeled by the graph below?

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

We have

a2 = 4

a3 = 2

a4 = 1

 calculate the difference

a3 - a2 = -2

a4 - a3 = -1

 The differences are not equal >the sequence is not arithmetic.

 Getting the ratio:

a3/a2 = 0.5

a4/a3 = 0.5

 The common ratio is 0.5. Using the general form for a geometric series:

an = a1 r^(n-1)

for n = 2 > a2=4

4 = a1 (0.5)^(2-1)

a1 = 8

therefore

an = 8 (1/2)^(n-1)

the answer is an = 8 (1/2)^(n-1)

the answer is none of those indicated in the question

14

step-by-step explanation:

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional