Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively.
Mathematics
oscar8338
Question
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively.
2 Answer

1. User Answers LammettHash
[tex]a_5=ra_4=r^2a_3=r^3a_2[/tex]
[tex]2304=36r^3\implies r=4[/tex]
Since [tex]a_2=ra_1\implies 36=4a_1\implies a_1=9[/tex], the sequence takes the form
[tex]a_n=(4)^{n1}a_1=9(4)^{n1}[/tex] 
2. User Answers joemommaflatduc
Answer:
[tex]a_n=9*4^n^^1[/tex]
Stepbystep explanation:
Substitute the value of n for the nth term
[tex]a_2=9*4^(^2^)^^1[/tex]
Subtract 1 from 2
[tex]a_2=9*4[/tex]
Multiply 9 by 4
[tex]a_2=36[/tex]
This is the only option from the choices that has a second term of 36 so it is the only option that satisfies the requirements.