Question

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

A) an=1/3⋅4^n−1

B) an=4(1/3)^n−1

C) an=4(1/3)^n

D) an=1/3⋅4^n

Answer 1

B) an=4(1/3)^n−1

Answer 2

ANSWER

The correct answer is B)


`a_n=4( (1)/(3) )^(n-1)`


Step-by-step explanation

The recursive formula for the geometric sequence is


`a_n= (1)/(3) a_(n-1)`
where,


`a_1 = 4`

This implies that,


`a_2= (1)/(3) a_(2-1)`



`a_2= (1)/(3) a_(1)`

`a_2= (1)/(3) * 4 = (4)/(3)`



The explicit rule is of the form,


`a_n=a_1r^(n-1)`
where


`r = ( a_(2))/( a_(1))`


`r = ( (4)/(3) )/( 4)`



`r = (4)/(3) * (1)/(4) = (1)/(3)`


The explicit rule is given by,


`a_n=4( (1)/(3) )^(n-1)`