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The sum of the odd numbers in an even-ending sequence is 2/5 of the total sum. The sum of an arithmetic sequence is
Sn = n(a1 + an)/2
Sn = n(a1 + an)/5
Sn = 400(1+400)/5
Sn = 32080
* * * * *
Very convincing but totally incorrect!
Simply try it out for the first 2 consecutive odd numbers:
1 + 3 = 4
1 + 2 + 3 = 6 but 4 is not 2/5 of 6!
The correct answer:
The nth odd number is 2n - 1
The sum of the 1st and 400th odd numbers is 2*1-1 + 2*400-1 = 2*401 - 2 = 2*400 = 800
The sum of the 2nd and 399th odd numbers is 2*2-1 + 2*399-1 = 2*401 - 2 = 2*400 = 800
there are 200 such pair so the grand total is 800*200 = 160,000
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