Question

Let \( e^{1/c}, e^{b/c}, e^{1/a} \) are in A.P. with a common difference \( d \). Then \( e^{1/c}, e^{b/c}, e^{1/a} \) are in:

• A. G.P. with common ratio \( e^d \)
• B. G.P. with common ratio \( e^{1/d} \)
• C. G.P. with common ratio \( e^{d(b^2 - d^2)} \)
• D. A.P.

Hint:

When terms are in arithmetic progression, they can be related to a geometric progression with a specific ratio.

Answer 1

The Correct Option is A

Using the properties of A.P. (Arithmetic Progression) and G.P. (Geometric Progression), we can deduce that the terms are in G.P. with a common ratio \( e^d \).
Final Answer: \[ \boxed{\text{G.P. with common ratio } e^d} \]