In a Geometric Progression, if the product of the first three terms is $$ \frac{27}{8} $$, then its second term is:

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Accepted Answer

1. **Let the terms of the GP**:  
   The three terms in a GP can be represented as $$ \frac{a}{r}, a, ar $$, where $$ a $$ is the middle term and $$ r $$ is the common ratio.

2. **Product of the terms**:  
   The product of these terms is:  
   $$
   \frac{a}{r} \cdot a \cdot ar = a^3
   $$

3. **Given condition**:  
   It is given that the product of the terms equals $$ \frac{27}{8} $$:  
   $$
   a^3 = \frac{27}{8}
   $$

4. **Solve for $$ a $$**:  
   Taking the cube root on both sides:  
   $$
   a = \sqrt{\frac{27}{8}} = \frac{\sqrt{27}}{\sqrt{8}} = \frac{3}{2}
   $$

5. **Conclusion**:  
   The second term (middle term) of the GP is $$ a = \frac{3}{2} $$.

Thus, the correct answer is **(a) $$ \frac{3}{2} $$**.

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