Question

In a Geometric Progression (G.P.), if the third term is 4, then the product of the first 5 terms is

• A. $4^3$
• B. $4^4$
• C. $4^5$
• D. None of these

Hint:

In a G.P., the product of terms equidistant from the beginning and end is always equal.

Answer 1

The Correct Option is B

Step 1: Write the general terms.
Let the G.P. be $a, ar, ar^2, ar^3, ar^4$.
Step 2: Use the given condition.
The third term is $ar^2 = 4$.
Step 3: Find the product of first five terms.
\[ a \cdot ar \cdot ar^2 \cdot ar^3 \cdot ar^4 = a^5 r^{10} \]
Step 4: Express in terms of the third term.
\[ (ar^2)^4 = 4^4 \]
Step 5: Conclusion.
The product of the first 5 terms is $4^4$.