SOLUTION: In an arithmetic progression, 8th term is 8 and sum of the first 16 terms is 144. Find the first term and the common difference

Algebra ->  Sequences-and-series -> SOLUTION: In an arithmetic progression, 8th term is 8 and sum of the first 16 terms is 144. Find the first term and the common difference       Log On


   

Question 934777: In an arithmetic progression, 8th term is 8 and sum of the first 16 terms is 144. Find the first term and the common difference
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
General term, A%5Bn%5D=A%5B1%5D%2Bd%2A%28n-1%29. This is the basic formula for arithmetic sequence.

Sum of terms, S=%28n%2F2%29%28A%5B1%5D%2BA%5Bn%5D%29. This formula can be derived and can also be found in your textbook used as a reference. S means SUM.

Problem description means ;
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%5B8%5D=8. The summation of the first sixteen terms is based on n=16.

The rest of the process is simplification.

system%28A%5B1%5D%2B7d=8%2C8%282A%5B1%5D%2B15d%29=144%29

system%28A%5B1%5D%2B7d=8%2C2A%5B1%5D%2B15d=18%29
two equations with two unknown variables. Solve the system.
HINT: Start with Elimination Method, for a faster solution process.