The given sequence is:

\[
\frac{1}{24}, \frac{1}{20}, \frac{1}{16}, \frac{1}{12}, \dots
\]

To find the next term, let's analyze the pattern. Notice that the denominators are decreasing in an arithmetic sequence:

\[
24, 20, 16, 12, \dots
\]

Each denominator decreases by 4:

\[
24 - 20 = 4, \quad 20 - 16 = 4, \quad 16 - 12 = 4
\]

Following this pattern, the next denominator will be:

\[
12 - 4 = 8
\]

Thus, the next term in the sequence is:

\[
\frac{1}{8}
\]

### Final sequence:
\[
\frac{1}{24}, \frac{1}{20}, \frac{1}{16}, \frac{1}{12}, \frac{1}{8}
\]

Would you like a more detailed explanation, or do you have any other questions?

### Related questions:
1. What is an arithmetic progression, and how is it applied here?
2. How can you determine the \(n\)-th term of a sequence with changing denominators?
3. Can sequences have a mix of arithmetic and geometric patterns?
4. How do you find the sum of an infinite series like this?
5. What are the different ways to express fractions in a sequence?

### Tip:
Always check whether the numerators or denominators follow a consistent pattern when analyzing a sequence of fractions.

Explore how to find the next term in the sequence 1/24, 1/20, 1/16, 1/12. Learn about arithmetic sequences, the pattern of denominators, and the formula for determining the nth term. Suitable 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