Question 934777
General term, {{{A[n]=A[1]+d*(n-1)}}}.  This is the basic formula for arithmetic sequence.


Sum of terms, {{{S=(n/2)(A[1]+A[n])}}}.  This formula can be derived and can also be found in your textbook used as a reference.  S means SUM.


Problem description means  {{{system(A[1]+(7)d=8,(16/2)(A[1]+(A[1]+d*(15)))=144)}}};
what you get when using the data from your problem description, of final n being n=16, and n=8 for the given term at index 8.  Note carefully, the eigth term is n=8 and is given as {{{A[8]=8}}}.  The summation of the first sixteen terms is based on n=16.  


The rest of the process is simplification.


{{{system(A[1]+7d=8,8(2A[1]+15d)=144)}}}


{{{system(A[1]+7d=8,2A[1]+15d=18)}}}
two equations with two unknown variables.  Solve the system.
HINT: Start with Elimination Method, for a faster solution process.