PreCalc help with sums. I will mark brainliest. (also can you explain WHY you got what answer you got? Thanks)

Answer:
8
Step-by-step explanation:
a = -4
r = 16/-4 = -4
Sn = a(r^n - 1)/(r - 1)
52428 = -4[(-4)^n - 1]/(-4-1)
(-4)^n - 1 = 65535
(-4)^n = 65536
Means n is even
(4)^n = 65536
nln(4) = ln(65536)
n = 8