Question

If \( a_1 = 3 \) and \( a_n = n \cdot a_{n-1} \), for \( n \geq 2 \), then \( a_6 \) is equal to

• A. 72
• B. 144
• C. 720
• D. 2160
• E. 4320

Hint:

In recursive sequences, calculate each term based on the previous term and the recurrence relation.

Answer 1

The Correct Option is D

Step 1: The recurrence relation is \( a_n = n \cdot a_{n-1} \). 
So, calculate the terms step by step: \[ a_2 = 2 \cdot a_1 = 2 \cdot 3 = 6 \] \[ a_3 = 3 \cdot a_2 = 3 \cdot 6 = 18 \] \[ a_4 = 4 \cdot a_3 = 4 \cdot 18 = 72 \] \[ a_5 = 5 \cdot a_4 = 5 \cdot 72 = 360 \] \[ a_6 = 6 \cdot a_5 = 6 \cdot 360 = 2160 \]