Question 1066380
Assuming you mean, "sequence" instead of "series".


General term:
{{{a+(n-1)d}}}
Index is n;
common difference each next term is d.


{{{(a+4d)+(a+6d)=38}}}
{{{2a+10d=38}}}
{{{a+5d=19}}}


Sum of first fifteen terms
{{{15(a+a+(15-1)d)/2=375}}}


{{{(15/2)(2a+14d)=375}}}


{{{15(a+7d)=375}}}


{{{a+7d=25}}}


Simplified system is  {{{system(a+5d=19,a+7d=25)}}}.
Solve this system.