Question 998498
.
Let  x  be a middle term of this arithmetic progression.


Then two other terms are  x-d  and  x+d,  where  d  is the common difference.


The sum of three members is   (x-d) + x + (x+d) = 3x.


It is  126,  hence,   x = {{{126/3}}} = 42.


Now,  we need to find  d.  For it,  we have another equation


{{{(42-d)^2 + 42^2 + (42+d)^2}}} = {{{126}}},     or


{{{42^2 -2*42*d + d^2 + 42^2 + 42^2^2 + 2*42*d + d^2}}} = {{{126}}},     or


{{{2d^2 + 3*42^2}}} = {{{126}}},


{{{2d^2}}} = {{{126 - 3*42^2}}}.


Hey,  the right side is negative!  While the left side is always non-negative. 


Your problem has no solution. 


Truly,  I spent my time for nothing,  working on this problem.