Question 827009
{{{a[1]=50}}}  and {{{d=-8}}}


{{{S[n]=(n/2)*(2*a[1]+(n-1)*d)=(d/2)*n^2+(a[1]-d/2)*n
}}}


so 
{{{
182=-4n^2+54n
}}}


which has only one suitable solution,   {{{n=7}}}   (why?)


checking...
 50+42+34+26+18+10+2=182