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

$a_n=(-4)^{n-1}a_1=9(-4)^{n-1}$

Answer 2

Answer:

$a_n=9*4^n^-^1$

Step-by-step 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.