Question

a, b, c, d and e are 5 distinct numbers that form an arithmetic progression. They are not necessarily consecutive terms but form the first 5 terms of the AP. It is known that c is the arithmetic mean of a and b, and d is the arithmetic mean of b and c. Determine which of the following statements is / are true in light of the above stated information?
i. Average of all 5 terms put together is c
ii. Average of d and e is not greater than average of a and b
iii. Average of b and c is greater than average of a and d

• A. i and ii only
• B. i and iii only
• C. ii and iii only
• D. ii only
• E. i, ii and iii

Hint:

Arithmetic Mean properties in an AP reflect physical distance on a number line. If $Y$ is the mean of $X$ and $Z$, $Y$ is physically equidistant from both. Use a simple number line to visualize term spacing.

Answer 1

The Correct Option is A