The sum of the first 3 terms of an AP is 6 and that of the last 3 terms is 16. If the AP has 13 terms, what is the Arithmetic mean of the three terms that are exactly at the middle of the progression?
Question and options
The sum of the first 3 terms of an AP is 6 and that of the last 3 terms is 16. If the AP has 13 terms, what is the Arithmetic mean of the three terms that are exactly at the middle of the progression?
Answer and explanation
Correct answer: B - \(\frac{11}{3}\)
The first 3 terms sum to 6, so a2 = 2; the last 3 sum to 16, so a12 = 16/3. The middle three (a6, a7, a8) have mean a7 = (a2 + a12)/2 = (2 + 16/3)/2 = 11/3.
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