Question

For a set of \( n \) integers in arithmetic progression, the difference between twice the median of the set and the range of the set is equal to twice the first term.

• A. Always
• B. Sometimes
• C. Never
  % Correct answer
• D.
• E.

Hint:

For arithmetic progressions, the relationships between the median, first term, and range follow specific properties that are consistent across all such sets.

Answer 1

The Correct Option is A

For an arithmetic progression, the median is the middle term, and the range is the difference between the largest and smallest terms. The difference between twice the median and the range can be shown as: \[ 2 \times \text{Median} - \text{Range} = 2 \times \text{First term} \] This equation holds true for all sets of \( n \) integers in arithmetic progression. Therefore, the correct answer is "Always".