The sum of the first 3 terms in an AP is 51 and that of the last 3 is 99. If the AP has 11 terms, what is the arithmetic mean of the middle 3 terms? A. 17B. 19C. 21D. 25

Solution

The AP can be expressed as a, (a + d), —, (a +10d).
The sum of the first 3 terms is (3a + 3d) = 51 and that of the last 3 is (3a + 27d) = 99.
Solving these equations, we get a = 15 and d = 2.
The arithmetic mean of the 3 terms is the value of the middle term = 25.