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Is the answer given wrong?

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by billzhao » Mon Feb 02, 2009 3:56 pm
Problem: The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?

The answer to the question is n=79.

but my calculation derives n = 159 based on S=a*(n-1)/2 + 1/2*(n-1)/2*((n-1)/2-1)*d = 79*80, where a=2 and d=2.

Any one can help?

Thanks!
Yiliang
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Source: — Problem Solving |


by mrsmarthi » Tue Feb 03, 2009 7:44 pm
We have rule to remember

Sum of first X even integers = X * (X + 1)

i.e 2 + 4 + 6 + ......2X = X*(X+1) or
2(1 + 2 + 3 ....+ x) = X*(x+1)


Given that n is odd. Hence n-1 should be the last even number.

Given, 2 + 4 + 6 +......(n-1)= 79 * 80.

i.e we have in total (n-1)/2 terms.

Substituing the above rule, we have (n-1)/2 * ((n-1)/2) + 1)= 79 * 80.

(n-1)/2 = 79 ==> n = 159.

I would go with N = 159.
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Thanks for your help!

by billzhao » Tue Feb 03, 2009 8:14 pm
Thanks for your help!
Yiliang
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