The average of 41 consecutive odd numbers is 49. What is the largest n

SOLUTION

Since the average of 41 consecutive odd numbers is 49. We know that, An A.P. in which no. of terms is odd, average of first term and last term, average of second term and second last term, average of third term and third last term and so on, is equal to the average of whole A.P. and middle term of that A.P. is equal to the average of whole A.P.
So the 49 will be the 21^st no. (middle number) of series. 
Required,
Largest number = 49 + 2 × 20 = 89.