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We can notice that in this case, the mean of the set of integers will be the same as the median, as it is increasing by 1

 

N cannot be even as, for example with N = 10, 11 through 20 will have a mean of a decimal.

If we make N = 9, 10 through 18 makes the mean 14.

If we make N = 11, 12 through 12 makes the mean 17.

If we make N = 13, 14 through 26 makes the mean 20.

 

So N = 13

This series is in arithmetic progression

with first no = N+1

Common difference = 1

(N)th term = 2N

Sum of N term = (N)/2 {2(N+1) + N-1}

= (N)(3N+1)/2

Average of this sum= (3N+1)/2

As per question

(3N+1)/2 = 20

3N+1 = 40

3N= 39

N= 13