Question

If for the harmonic progression, \( t_7 = \frac{1}{10}, \, t_{12} = \frac{1}{25}, \) then \( t_{20} = \)

• A. \( \frac{1}{48} \)
• B. 49
• C. \( \frac{1}{49} \)
• D. 48

Hint:

For a harmonic progression, use the formula for the terms of the corresponding arithmetic progression.

Answer 1

The Correct Option is C

Step 1: Use the formula for harmonic progression.
For a harmonic progression, the terms are the reciprocals of the terms of an arithmetic progression. Using the given terms, we can find the common difference of the arithmetic progression.
Step 2: Find \( t_{20} \).
By applying the formula for the harmonic progression, we find: \[ t_{20} = \frac{1}{49} \]
Step 3: Conclusion.
Thus, \( t_{20} = \frac{1}{49} \), corresponding to option (C).