Question

OK I need help the answer is c but I didn't understand the teacher explanation pls help me

Answer 1

9 - 6 + 4 - 8/3 ..,
geometric series a(n) = a1r^(n-1)

r = a(n+1)/a(n)
-6/9 = -2/3
4/-6 = -2/3
-8/3/4 = -2/3
so r = -2/3 and a1 = 9

Sn = a1(1-r^n)/(1-r) = 9(1-(-2/3)^n)/(1-(-2/3))
n is infinite Sn = 9/(5/3) = 27/5