If the middle term of G.P series having 3 term is 6 and if the sum of first and 3rd then detrmine the three numbers ?

Use your GP formula:

T_n = ra^{n-1}

T_2 = 6 = ra^{2-1}

T_1 + T_3 = ra^{1-1} + ra^{3-1}

S_3 = T_1 + T_2 + T_3 = \frac{a(1-r^n)}{1-r}

n = 3

I think that you have enough equations.