# A question on Property of 3 positive numbers

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Dear all, suppose I have 3 positive numbers in order N1 < N2 < N3. Then can I say that, this inequality will always hold: (N1 + N3) > 2*(N2).

Thanks for your time.

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You should be able to figure this out with even a trivial test case.....

1 < 500 < 501

(1 + 501) > 2*500
502 > 1000

false.

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If we make a couple of changes like saying that the difference between N1 and N2 is equal to the difference between N2 and N3 such that (lets call the difference here 'k'):
n < n+k < n+k+k
Then,
N1 + N3 = (n + n + k +k) = 2n + 2k
and
2*N2 = 2*(n + k) = 2n + 2k
Then you could say that:
2n+2k = 2n+2k

I just thought it was neat, but I wonder what the problem the OP's question came from.

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The best part of the OP's question is that N1=1, N2=2, N3=3 is a counterexample. I wonder how hard he tried to find one...

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Rutin
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