$\begin{align}  & \text{Let the positive integer be }a-d,a,a+d \\ & \text{Sum of the A}\text{.P}=a-d+a+a+d=21 \\ & 3a=21,\text{ }a=7 \\ & \text{Sum of the square of the A}\text{.P} \\ & {{(a-d)}^{2}}+{{a}^{2}}+{{(a+d)}^{2}}=155 \\ & {{a}^{2}}-2ad+{{d}^{2}}+{{a}^{2}}+{{a}^{2}}+2ad+{{d}^{2}}=155 \\ & 3{{a}^{2}}+2{{d}^{2}}=155 \\ & \text{substitute }7\text{ for }a\text{ in }3{{a}^{2}}+2{{d}^{2}}=155 \\ & 3{{(7)}^{2}}+2{{d}^{2}}=155 \\ & 2{{d}^{2}}=155-147=8 \\ & {{d}^{2}}=4,\text{ }d=\pm 2 \\ & \text{The number are }5,7,9 \\\end{align}$