Find the sum of the first five terms of the geometric series in which a2 is - 12 and a5 is 768

Hello:

the general term is : an = ap*q^ (n-p) ... q : common ratio

n=5 and p=2 : a5 = a2*q^ (5-2)

768 = - 12q^3

q^3 = 768 / (-12)

q^3 = - 64

but : 64 = 4^3

q^3 = (-4) ^3 ... - 4^3 = ( - 4) ^3

q = - 4

calculate the first term : a1

a2 = a1 q

a1 = a2/q

a1 = - 12/-4

a1 = 3

the sum of the first five terms is : S = a1 * (1 - q^n) / (1 - q)

a1 = 3 q = - 4 n = 5

S = 3 (1 - (-4) ^5) / (1 - (-4)) ... calculate