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
1 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]