you are following the old text book a wt that is not x+b that is x+6

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you are following the old text book a wt that is not x+b that is x+6

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Here x , x+2 & x+b are three consecutive numbers in G.P

Therefore

Therefore

Or,

Therefore

Therefore

Or,

the answer is

if x, x+2,x+b are in GP then there common ratio is equal then

a₂/a₁ = a₃/a₂

then x+2/x = x +b/ x+2

= (x+2)² = x² +bx

=x²+4x+4 = x²+ bx

= 4x+4 = bx

= 4x-bx = -4

= x(4-b) = -4

= x = -4 / 4-b

then according to the new text book the answer is

if the x , x+2 , x+6 are in GP

then

x+2/x = x+6/x+2

= (x+2)²=x²+6x

= x²+4x+4 = x²+6x

= 4x+4 = 6x

= 4x-6x = -4

= -2x = -4

= x = -4/-2

= x =2

then x,x+2,x+6 are 2,4,8

there are in GP.