If (3-x) +(6)+(7-5x) is a geometric series, find two possible values for
A,x
B,the common ratio
C,the sum of the GP
we need to have:
6/(3-x) = (7-5x)/6
(3-x)(7-5x) = 36
21 - 22x + 5x^2 - 36 = 0
5x^2 - 22x - 15 = 0
(x-5)(5x + 3) = 0
x = 5 or x = -3/5
if x = 5, the series is -2 + 6 - 18 = -14 and r = -3
if x = -3/5, the series is 18/5 + 6 + 10 = 62/3 , and r = 5/3
check my arithmetic