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

ANSWER

The explicit formula that defines the sequence is
$f(n) = 3 ( \frac{1}{3} ) ^{n - 1}$


EXPLANATION


The given sequence is
$3,1, \frac{1}{3} , \frac{2}{9} ,...$


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
$r = \frac{1}{3}$


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,



$f(n) = 3( \frac{1}{3} )^{n - 1}$


The correct answer is option D.

Answer 2

Answer:

D

Step-by-step explanation: