Question

Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are -36 and 2304, respectively

Answer 1

`a_5=ra_4=r^2a_3=r^3a_2`

`2304=-36r^3\implies r=-4`

Since
`a_2=ra_1\implies -36=-4a_1\implies a_1=9`, the sequence takes the form


`a_n=(-4)^(n-1)a_1=9(-4)^(n-1)`