The sum of the first 10 terms of the geometric sequence -4, 6, -9,..., to the nearest tenth, is;

Question

The answer is:
For the geometric series a=-4, r=-1.5 or -3/2, n=10.
Sn= a(r^n - 1)/r - 1

S10= -4((-1.5)^10 - 1)/-1.5 - 1

S10= 90.7

My question is from where they got r=-1.5 or -3/2 Please can somebody tell me why!!!

Answer 1

6/-4 = -1.5 = r

-9/6 = -1.5 = r

r is the ratio of every term to the one before it.