Answer:
[tex]a_n=9(4^{n-1})[/tex]
Step-by-step explanation:
we know that
In a Geometric Sequence each term is found by multiplying the previous term by a constant, called the common ratio (r)
In this problem we have
[tex]a_2=36\\ a_5=2,304[/tex]
Remember that
[tex]a_2=a_1(r)[/tex] -----> [tex]36=a_1(r)[/tex] -----> equation A
[tex]a_5=a_4(r)[/tex]
[tex]a_5=a_3(r^{2})[/tex]
[tex]a_5=a_2(r^{3})[/tex]
Substitute the values of a_5 and a_2 and solve for r
[tex]2,304=36(r^{3})[/tex]
[tex]r^{3}=2,304/36[/tex]
[tex]r^{3}=64[/tex]
[tex]r=4[/tex]
Find the value of a_1 in equation A
[tex]36=a_1(4)[/tex]
[tex]a_1=9[/tex]
therefore
The explicit rule for the nth term is
[tex]a_n=a_1(r^{n-1})[/tex]
substitute
[tex]a_n=9(4^{n-1})[/tex]
