Question

Consider the sequence below.

3, 1, 1/3, 1/9,...

select the explicit function which defines the sequence.

A.) f(n) = 1/3 • 2^(n - 1)

B.) f(n) = 2 • (1/3)^(n - 1)

C.) f(n) = 1/3 • 3^(n - 1)

D.) f(n) = 3 • (1/3)^(n - 1)

Answer 1

D

Explanation:

Answer 2

ANSWER

The explicit formula that defines the sequence is

`f(n) = 3 ( (1)/(3) ) ^(n - 1)`


EXPLANATION


The given sequence is

`3,1, (1)/(3) , (2)/(9) ,...`


The first term of this sequence is

`a = 3`
We can find the common ratio by expressing a subsequent term over a previous term and simplifying it.


The common ratio is

`r = (1)/(3)`


The formula for finding the nth term of the given geometric sequence is given by,


`f(n) = a {r}^(n - 1)`




We now substitute the value of the first term and the common ratio in to the above formula to obtain,




`f(n) = 3( (1)/(3) )^(n - 1)`


The correct answer is option D.