Which sequence is modeled by the graph below? coordinate plane showing the points 1, 4; 2, 0.8; and 3, 0.16

This question comes with a set of answer choices:

a) An = 4 (-5)^ (n-1)

b) An = 4 ((1/5) ^ (n -1)

c) An = 0.4 (5)^ (n - 1)

d) An = (1/5) (4)^ (n -1)

The data are:

number of term             term

1                                    4

2                                    0.8

3                                    0.16

n                                   4 (1/5)^ (n-1)

Given that the first term is 4 you can disscard the options c) and d) because their first terms are 0.4 and 1/5.

Given that the option a) alternates positive and negative terms you can discard it too.

Now test the option b) An = 4 (1/5) ^ (n-1)

n           An = 4(1/5) ^ (n - 1)

1           A1 = 4(1/5) ^0 = 4

2           A2 = 4(1/5)^1 = 4/5 = 0.8

3            A3 = 4(1/5)^2 = 4/25 = 0.16

So, the sequence An = 4(1/5)^(n-1) models the graph.

An = 4 (1/5)^ (n-1)