Mathematics: Consider the sequence below. 3, 1, 1/3, 1/ 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)

7 divided by 22 is 0.318 rounded to the nearest thousandth...

Consider the sequence below. 3, 1, 1/3, 1/ select - id31131350179, taleiayarbough4544

Ответ:

natalie2sheffield

10.03.2022

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.

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Consider the sequence below. 3, 1, 1/3, 1/ 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)

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