b-a = 2-a (From AP)
b = 2a -2 (1)
9/b = b/a (From GP)
9a = b^2 (2)
Sub (1) into (2)
9a = (2a-2)^2
9a = 4a^2 - 8a + 4
0 = 4a^2- 17a + 4
0 = (4a-1)(a-4)
a= 1/4, 4
put in (1)
b=2a-2
b= 6, when a =4
b = -3/2, when a = 1/4
Limiting sum is when |r| < 1.
The r in this is y.
So y must be...