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

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.