Question

If three terms are x-2,x-1 and 3x-5 in G.P.find the possible values of r

Answer 1

Answer:

x,2x+2,3x+3 are in G.P. Hence,

(2x+2)2=x(3x+3)

⇒4x2+8x+4=3x2+3x

⇒x2+5x+4=0

⇒x=−1, −4

So, the G.P. is −4,−6,−9,.... (considering x = -4, as for x = -1, 2x + 2 = 0). 

Hence, the fourth term is −9×1.5=−13.5.