this quest requires some concept of function chapter
let the no be
A-d, A, A+d, b (in increasing order)
as given b-(A-d)=30
b=30+A-d now numbers
A-d, A, A+d, 30+A-d
apply gm formula
A*(30+A-d)=(A+d)^2
........after solving u will get
, as A>0 then
10-d>0......., 10>d
and all terms are postive thus d>0 and it must be divisible by 3 because A is a integer
so we have options for d ------ 3, 6, 9
but A-d>0 (all terms are +VE)
A>d, 
d>30-d , d>7.5
so finally we will take d=9 and then
A=27 numbers are
18 ,27 ,36, 48
their sum =129


