Question

For a GP, \( a_n = 3(2^n) \), \( n \in \mathbb{N} \), Find the common ratio.

• A. 2
• B. 1/2
• C. 3
• D. 1/3

Hint:

The common ratio of a geometric progression can be found by comparing the general term with the given expression.

Answer 1

The Correct Option is A

Step 1: Formula for the general term of a GP.
The general term for a geometric progression is given by: \[ a_n = a_1 r^{n-1} \] By comparing the given formula \( a_n = 3(2^n) \) with the general term formula, we can determine that the common ratio \( r = 2 \).
Step 2: Conclusion.
Thus, the common ratio is 2.
Final Answer: \[ \boxed{2} \]