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

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