Question

What is the explicit rule for this geometric sequence? a1=4; an=1/3⋅an−1

Answer 1

ANSWER

The correct answer is B)

$a_n=4( \frac{1}{3} )^{n-1}$


EXPLANATION

The recursive formula for the geometric sequence is

$a_n= \frac{1}{3} a_{n-1}$
where,

$a_1 = 4$

This implies that,

$a_2= \frac{1}{3} a_{2-1}$


$a_2= \frac{1}{3} a_{1}$
$a_2= \frac{1}{3} \times 4 = \frac{4}{3}$



The explicit rule is of the form,

$a_n=a_1r^{n-1}$
where

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

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


$r = \frac{4}{3} \times \frac{1}{4} = \frac{1}{3}$


The explicit rule is given by,

$a_n=4( \frac{1}{3} )^{n-1}$