(2+x,\ 5+x,\ 9+x) in H.P.

[ \dfrac{1}{2+x},\dfrac{1}{5+x},\dfrac{1}{9+x}\text{ in A.P.} ] [ \dfrac{2}{5+x}=\dfrac{1}{2+x}+\dfrac{1}{9+x}=\dfrac{11+2x}{(2+x)(9+x)} ] [ 2(2+x)(9+x)=(5+x)(11+2x) ] [ 2(18+2x+9x+x^2)=55+10x+11x+2x^2 ] [ 36+22x+2x^2=55+21x+2x^2 ] [ 36+22x=55+21x\implies x=19 ]

Answer: (x=19)