Question

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

Answer 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