UGC NET Questions (Paper – 1)

This option is correct because three consecutive integers can be written as n−1, n and n+1. Their sum is (n−1) + n + (n+1) = 3n. Dividing by 3 gives n, which is the middle integer. Therefore, the average equals the middle integer.

Option A:
The smallest integer in the set is n−1. The average of n−1, n and n+1 is n, which is larger than the smallest. Thus, the average cannot equal the smallest integer.

Option B:
The largest integer in the set is n+1. Since the average is n, which lies between n−1 and n+1, it is less than the largest value. Therefore, it is not equal to the largest integer.

Option C:
Saying the average equals the sum of the integers would ignore the division by the number of terms. The sum is 3n, while the average is 3n ÷ 3 = n. Thus, "sum of" does not describe the average correctly.

Option D:
The middle integer n is exactly the average of the three consecutive integers. It balances the smaller and larger values symmetrically. Hence, the average is always equal to the middle integer, making this option correct.