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_n=9*4^n^-^1`

Explanation:

Substitute the value of n for the nth term

`a_2=9*4^(^2^)^-^1`

Subtract 1 from 2

`a_2=9*4`

Multiply 9 by 4

`a_2=36`

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.

Answer 2

`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)`