Math Problem Statement

1/24,1/20,1/16,1/12,...?

Solution

The given sequence is:

124,120,116,112,\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:

24,20,16,12,24, 20, 16, 12, \dots

Each denominator decreases by 4:

2420=4,2016=4,1612=424 - 20 = 4, \quad 20 - 16 = 4, \quad 16 - 12 = 4

Following this pattern, the next denominator will be:

124=812 - 4 = 8

Thus, the next term in the sequence is:

18\frac{1}{8}

Final sequence:

124,120,116,112,18\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 nn-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.

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Fractions
Patterns

Formulas

nth term of an arithmetic sequence: a_n = a_1 + (n-1)d

Theorems

Arithmetic Progression

Suitable Grade Level

Grades 6-8