SOLUTION: How many terms has an arithmetic {{{highlight(cross(progreression))}}} <U>progression</U> where sum is 1340 with first term 3 and nth term 131?

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Question 1149896: How many terms has an arithmetic highlight%28cross%28progreression%29%29 progression where sum is 1340 with first term 3 and nth term 131?
Answer by ikleyn(52874) About Me  (Show Source):
You can put this solution on YOUR website!
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For any arithmetic progression of n terms  a%5B1%5D, a%5B2%5D, a%5B3%5D . . . a%5Bn%5D,  the formula for its sum S works


    S = %28%28a%5B1%5D+%2B+a%5Bn%5D%29%2F2%29%2An.


In our case, it gives


    1340 = %28%283+%2B+131%29%2F2%29%2An = %28134%2F2%29%2An.


Hence,


    n = %282%2A1340%29%2F134 = 2*10 = 20.   


ANSWER.  The number of the terms in the progression is 20.

Solved.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".


Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.