If x,2x+2,3x+3 are in GP, then the fourth term is
A. 27
B. -27
C. 13.5
D. -13.5
Answer: Option D
Solution (By Examveda Team)
x,2x+2,3x+3 are in Gp
i.e 2x+2 /2= 3x+3 / 2x+2
(2x + 2)2 = (3x+3)x
4x2 + 4+8x - 3x2 -3x =0
x2 +5x +4=0
x2 + 4x + x+4=0
x(x+4) +1(x+4)=0
x= -1,-4
when x=-1
numbers are -1 , 0 , 0 , this means r=0 so fourth term is also 0
i.e -1 ,0,0,0
when x=-4
GP series is -4 , -6 , -9 ,then r= 3/2
fourth term = ar3 = -4 * 27 /8 = -27 /2 or -13.5
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