for it to be in geometric sequence, it should be that
(x+11)/(5x+1) = (5x+1)/(x+2)
so that they will have the same r or common ratio
(x+11)/(5x+1) = (5x+1)/(x+2)
cross multiply
(x+11)(x+2) = (5x+1)(5x+1)
x^2 + 2x + 11x + 22 = 25x^2 + 5x + 5x + 1
x^2 + 13x + 22 = 25x^2 +10x +1
transpose all the terms in the left side to the right side
25x^2 - x^2 +10x -13x +1 - 22 =0
24x^2 -3x -21 = 0
(8x+7)(3x-3) = 0
(8x+7)=0
8x = -7
x= -7/8
3x-3 =0
3x=3
x=1
