An arithmetic progression is one in which each subsequent term is the

The arithmetic progression could be integers, even integers, mulriples of 6 . . .

This progression has an even number of terms. The questions are centered around median, mean, and integers. Consecutive integers will NOT yield an integer for mean or median if number of terms is even, so try

2, 4, 6, 8, 10, 12

as an example. (We are trying to disprove each statement). Evaluate: what MUST be true?

I. The average is not an integer.
The average here is 7, an integer.
Sum of 42/6 = mean of 7. OR
mean = median = 7. REJECT

II. The median is not an integer.
The median, between the 3rd and 4th terms, is also 7. REJECT

III. The median and the mean are equal.
ALWAYS the case in an arithmetic progression.

Answer B