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