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Sum of even numbers

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Sum of even numbers

by muna_m » Fri Jun 19, 2009 12:16 pm
The sum of the even numbers between 1 and n is 79*80, where n is an odd number, then n=?

I know we can solve it using AP. But, I approached it using no. of terms & average and was stuck.

No. of terms (even) = (n-1-2)/2 = (n-1)/2 terms

Average = (2+n-1)/2 = (n+1)/2

Thus,Sum = No of terms * Avg
79 * 80 = (n-1)/2 * (n+1)/2
79 * 80 * 4 = n^2 - 1

And solving for n seems hard. Where did i go wrong?! Isn't this method viable for this question?
Any help would be greatly appreciated :)
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by shanmugam.d » Sat Jun 20, 2009 1:18 am
Hi, it can be solved as follows:

Since n is an odd number, let us represent it as n = 2m + 1

so the summation of all even numbers from 1 to n can be written as

2 + 4 + 6 + .... + 2m
= 2 * (1 + 2 + 3 + .... + m)
= 2 * (m*(m+ 1))/2
= m * (m+1)
= 79 *80

Therefore m = 79

n= 2m + 1 = 2*79 + 1 = 159
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by muna_m » Sat Jun 20, 2009 3:08 pm
The OA 79

I got 159 too using my method so was wondering where i went wrong..
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by zenithexe » Sun Jun 21, 2009 2:41 am
Hey, I think its typo (if that's ever possible)

if you use the answer value to calculate the sum it will be 19.5*80, maybe the typer got confused?
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sum of even series

by ksb214 » Mon Jun 22, 2009 6:13 am
use formula for arithmatic progression

Sum = n(2a + (n-1)d )/2

a = first term
d= difference between consecutive numbers

here a = 2 and d = 2

sum = n(2*2 + (n-1)*2)/2
sum = n(2+2n)/2
sum = n(n+1) = 79*(80)

Hence n = 79
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by zenithexe » Mon Jun 22, 2009 10:58 pm
Hey, Thanks for the input.

though, the "n" found on your solution mean's 'n'th number of the sequence, not the actual n asked in the question.

so n=79 means 79th number of sequence 2,4,6,8,....

which means the actual n asked in the question would be n=2*79+1=158+1 or 159



I think that's maybe where the writer got confused too, or maybe we're missing some info on the question.
Thanks for mentioning the arithmatic progression I didn't know that formula until now.

PS.To be honest, I actually used excel to confirm that 159 is indeed the correct answer.
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