A finite arithmetic sequence has 7 terms, and the first term is 3/4

A finite arithmetic sequence has 7 terms, and the first term is 3/4. What is the difference between the mean and the median of the 7 terms?

  1. 0
  2. 3/4
  3. 4/3
  4. 3
  5. 4

Answer

The correct answer is A.

First term, a = 3/4

Total terms, n = 7

Common difference = d

The nth term = a + (n - 1)d

The median is the middle term, or 4th term = 3/4 + 3d

The mean is the sum of all the terms divided by 7.

Sn =  n/2 [2a + (n - 1)d]

Sn = 7/2 [3/2 + 6d]

Mean = Sn/7

Mean = 3/4 + 3d

Because the mean and the median are both 3/4 + 3d, their difference is 0.