Best Answer

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

Q: What is the sum of the first 400 consecutive odd numbers?

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