Enter the explicit rule for the geometric sequence.3/2, 3/4, 3/8, 3/16, 3/32, …a(n)=

Ответ:

guilloryjamira

10.03.2022

ANSWER

The explicit formula is
$a_n= \frac{3}{2} ({ \frac{1}{2} })^{n - 1}$

EXPLANATION

The given geometric sequence is
$\frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \frac{3}{16}, \frac{3}{32}$

The explicit formula is given by,

$a_n = a_1 ({r})^{n - 1}$

where the first term is
$a_1 = \frac{3}{2}$

and the common ratio is

$r = \frac{a_2}{a_1}$

$r = \frac{ \frac{3}{4} }{ \frac{3}{2} }$

This implies that,

$r = \frac{3}{4} \times \frac{2}{3}$

$r = \frac{1}{2}$

We now substitute all these values in to the formula to obtain,

$a_n= \frac{3}{2} ({ \frac{1}{2} })^{n - 1}$

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Enter the explicit rule for the geometric sequence.3/2, 3/4, 3/8, 3/16, 3/32, …a(n)=

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