Question 826126
Setting up our equations we find:

{{{192=(n/2)(a[1]+27)}}}  and  {{{27=a[1]+(n-1)*2}}}


Solving the system by substitution leads to two possible solutions, both valid.

{{{a[1]=5}}}, {{{n=12}}}


or

{{{a[1]=-3}}}, {{{n=16}}}