https://file.aiquickdraw.com/mathbot/file/17342583004501jnb3x7k.jpg

### Problem Breakdown

The question asks for the **3rd term** in the geometric sequence generated by the rule \( 5^n \), where \( n \) represents the position in the sequence.

### Step-by-Step Solution

1. **Formula**: The sequence is defined by the rule \( 5^n \), where \( n = 1, 2, 3, \dots \). The nth term of the sequence is \( a_n = 5^n \).

2. **Find the 3rd term**:
   Substitute \( n = 3 \) into the rule:
   \[
   a_3 = 5^3
   \]

3. **Simplify**:
   \[
   5^3 = 5 \times 5 \times 5 = 125
   \]

### Final Answer:
The **3rd term** in the geometric sequence is **125**.

---

Would you like further clarification or an exploration of geometric sequences?

---

### Related Questions:
1. What is the 5th term in the sequence \( 5^n \)?
2. How would you find the ratio between consecutive terms of \( 5^n \)?
3. What is the general formula for the sum of the first \( n \) terms in a geometric sequence?
4. How does the growth of \( 5^n \) compare to \( 3^n \)?
5. If the sequence starts with \( n = 0 \) instead of \( n = 1 \), what is the new 3rd term?

### Tip:
In geometric sequences where terms grow exponentially, the **common ratio** plays a crucial role—it tells you how much each term is multiplied to get the next one. For \( 5^n \), the common ratio is always \( 5 \).

Work out the 3rd term in the geometric sequence generated by the rule 5^n.

Learn how to calculate the 3rd term of the geometric sequence defined by the rule 5^n. This problem demonstrates the use of exponents and the structure of geometric sequences. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation