SOLUTION: Given the arithmetic series 2+4+6...=420 find the term a and the common difference

Question 1052919: Given the arithmetic series 2+4+6...=420 find the term a and the common difference
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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Given the arithmetic series 2+4+6...=420 find the term a and the common difference
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1.  The common difference is 2.


2.  To find the number of terms, first cancel the given equality by 2. You will get

    1 + 2 + 3 + . . . +  = 210.

    Or, which is the same,

     = 210,

    n*(n+1) = 420.

    420 decomposes into the product of two consecutive natural integers by an unique way: 420 = 20*21.

Answer.  The common difference is 2.
         The number of terms is 20.
         The 20-th term is  = 2 + 2*(20-1) = 2 + 38 = 40.

On arithmetic progressions, see the lessons
My lessons on arithmetic progressions in this site are
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and arithmetic progressions
    - One characteristic property of arithmetic progressions
    - Solved 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".

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