Sequences And Series — Easy JEE math MCQ
If the arithmetic mean and geometric mean of two positive numbers are 10 and 8 respectively, then the harmonic mean of these numbers is:
- A. 5.6
- B. 6.4
- C. 7.2
- D. 8.0
Solution
For two positive numbers, the relationship between AM, GM, and HM is:
\[
\text{GM}^2 = \text{AM} \times \text{HM}
\]
Therefore:
\[
\text{HM} = \frac{\text{GM}^2}{\text{AM}} = \frac{8^2}{10} = \frac{64}{10} = 6.4
\]
So the correct option is B.