SOLUTION: in an arithmetic series, the second to last term is three times the fifth term, the sum of the first eight terms equals 136, and the fourteenth term equals the twentieth minus the

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Question 932868: in an arithmetic series, the second to last term is three times the fifth term, the sum of the first eight terms equals 136, and the fourteenth term equals the twentieth minus the second term. Determine how many terms are in the arithmetic series.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
in an arithmetic series, the second to last term is three times the fifth term, the sum of the first eight terms equals 136, and the fourteenth term equals the twentieth minus the second term. Determine how many terms are in the arithmetic series.
Use formulas

 and ,

>>the second to last term is three times the fifth term<<

[That's a little bit ambiguous, because "second to last" might be
interpreted as "second FROM the last"; however I will interpret
it as "NEXT TO the last"]

>>the sum of the first eight terms equals 136<<

>>and the fourteenth term equals the twentieth minus the second term.<<












So we have the system of equations:

 

Solve that by substitution and get:

, ,  

There are 24 terms.

Edwin
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