Question

Which sequence is modeled by the graph below? coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8)

a. an = 1(2)n − 1
b. an = 2(1)n − 1
c. an = 1 + (2)n − 1
d. an = (2)(n − 1)

Answer 1

Answer: The correct option is d.

Step-by-step explanation:

From the given information it is noticed that the coordinate plane showing the points (1, 1) (2, 2) (3, 4) and (4, 8).

The coordinates are in the form of (x,y), it means the value of xth term of the sequence is y.

The point (1,1) represents that the first term is 1. Similarly from (2, 2) (3, 4) and (4, 8) points we can say that the second term is 2, third term is 4 and fourth term is 8.

The sequence is 1,2,4,8.

It can be written as,

`2^0,2^1,2^2,2^3`

Since the base is common that is 2 and the power is one less than the position of term. So the sequence is in the form of,

`a_n=2^(n-1)`

Therefore, the correct option is d.

Answer 2

The y-values of 1, 2, 4, 8 imply an exponential function of base 2. At n = 1, y = 1 = 2^0. We can substitute into the various choices to determine the correct equation, which turns out to be a_n = 2^(n-1).