https://file.aiquickdraw.com/mathbot/file/1730135436681vvvbfnho.jpg

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.

List the first five terms of the sequence where a_1 = 12 and a_(n+1) = a_n / n.

Explore how to find the first five terms of a recursive sequence given a_1 = 12 and a_(n+1) = a_n / n. This problem covers fundamental concepts of sequences and recursion, ideal for high school students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation