I found this question-n-answer on net and somehow not convinced with the question -- seems question was not put "accurately", not the way it was solved.

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Ques: The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?

Sol: First term a=2, common difference d=2 since even number
an = a1 + (n - 1)d, n = 1, 2, ...
therefore sum to first n numbers of Arithmetic progression would be
n/2(2a+(n-1)d)
= n/2(2*2+(n-1)*2)=n(n+1) and this is equal to 79*80
therefore n=79 which is odd...
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In the question, it says "n is an odd number" and so it's pointing that n is the value of nth term and not the value of n (i.e. # of terms in the series). However, in solution, it used "n" as the # of terms in the series -- which is wrong.

As I understand,
Series would be: 2, 4, 6, 8 ..... (n-1)
getting # of terms (x) in the series:
n-1 = 2 + (x-1)* 2 => n-1 = 2 + 2x - 2 = 2x ==> x = (n-1)/2
therefore Sum = x/2 [ 2*2 + (x-1)*2] = (n-1)/4 [ 4 + 2x - 2] = (n-1)/4 [2 + 2x] = (n-1)/2 [x+1]
= (n-1)/2 [ (n-1)/2 +1 ] = (n-1)2 [ (n+1)/2] = ( n square - 1 ) / 4 = 79*80
==> n square = 79*80*4 +1 ==> n = 159 which is odd number

Can someone verify and reconfirm? Thanks