Find the common ratio and write out the first four terms of the geometric sequence (1.04)^(n -1)

Common ratio is
a1=
a2=
a3=
a4=

The given sequence is \( a_n = (1.04)^{n-1} \), which represents a geometric sequence. In a geometric sequence, the common ratio is the constant factor between consecutive terms, and the first term is obtained when \( n = 1 \).

### Solution:
1. **Common Ratio (\(r\))**:
   In any geometric sequence given in the form \( a_n = ar^{n-1} \), \( r \) is the base of the exponential function. Here, \( r = 1.04 \).

2. **First Four Terms (\(a_1, a_2, a_3, a_4\))**:
   - \( a_1 = (1.04)^{1-1} = (1.04)^0 = 1 \)
   - \( a_2 = (1.04)^{2-1} = (1.04)^1 = 1.04 \)
   - \( a_3 = (1.04)^{3-1} = (1.04)^2 = 1.0816 \)
   - \( a_4 = (1.04)^{4-1} = (1.04)^3 = 1.124864 \)

### Final Answer:
- **Common Ratio**: \( r = 1.04 \)
- \( a_1 = 1 \)
- \( a_2 = 1.04 \)
- \( a_3 = 1.0816 \)
- \( a_4 = 1.124864 \)

Would you like detailed explanations for how these terms were calculated, or have any other questions?

---

**Related Questions:**
1. How can you generalize a geometric sequence formula for any term \( n \)?
2. What happens to the terms of this sequence as \( n \to \infty \)?
3. What is the sum of the first 10 terms of this sequence?
4. How would you express the \( n \)-th term if the common ratio was negative, e.g., \( r = -1.04 \)?
5. How do geometric sequences differ from arithmetic sequences?

**Tip:** In geometric sequences, multiplying by the common ratio repeatedly builds the sequence—knowing \( r \) allows you to predict any term!

Find the common ratio and write out the first four terms of the geometric sequence (1.04)^(n -1)

Learn how to find the common ratio and calculate the first four terms of the geometric sequence (1.04)^(n-1). This problem explains the properties of geometric sequences and how to use the formula to solve for specific terms. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation