Question

Which sequence is modeled by the graph below?

coordinate plane showing the points 2, 1; 3, 2; 4, 4; and 5, 8

an = one half(2)n − 1
an = 2(2)n − 1
an = 4(−2)n − 1
an = 2(one half)n − 1

Answer 1

First, we inspect what type of sequence is the order of the coordinates:
a2 = 1
a3 = 2
a4 = 4

Getting the difference,
a3 - a2 = 1
a4 - a3 = 2

The differences are not equal; hence, the sequence is not arithmetic.

Getting the ratio:
a3/a2 = 2
a4/a3 = 2

The common ratio is 2. Using the general form for a geometric series:
an = a1 r^(n-1)
If n = 2
1 = a1 (2)^(2-1)
a1 = 1/2

So,
an = (1/2) (2)^(n-1)

The answer is the first option.