To solve this sequence problem, let's analyze the terms one by one using the recursive formula:

Given:

• $a_1 = 12$
• $a_{n+1} = \frac{a_n}{n}$

We will calculate each term from $a_2$ to $a_5$ by applying the formula iteratively.

1. $a_1 = 12$ (already given)

2. $a_2 = \frac{a_1}{1} = \frac{12}{1} = 12$

3. $a_3 = \frac{a_2}{2} = \frac{12}{2} = 6$

4. $a_4 = \frac{a_3}{3} = \frac{6}{3} = 2$

5. $a_5 = \frac{a_4}{4} = \frac{2}{4} = 0.5$

Answer:

The first five terms of the sequence are:

• $a_1 = 12$
• $a_2 = 12$
• $a_3 = 6$
• $a_4 = 2$
• $a_5 = 0.5$

Would you like further explanation or have any questions?

Follow-up Questions:

1. What would be the sixth term, $a_6$, in this sequence?
2. How does the term $a_n$ change as $n$ increases in this recursive sequence?
3. Can you derive a general formula for the $n$-th term based on this sequence rule?
4. How would the sequence differ if the initial value $a_1$ was a different number?
5. What are some practical applications of recursive sequences in mathematics?

Tip: Recursive sequences are often easier to calculate when you take each step slowly and check each intermediate result.