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
Sum of even numbers
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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
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
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.
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.