Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.)
10, 22, 34, 46, 58,
The next number is

Let's examine the sequence:  
\[ 10, 22, 34, 46, 58 \]

### Step 1: Calculate the differences between consecutive terms:
- \( 22 - 10 = 12 \)
- \( 34 - 22 = 12 \)
- \( 46 - 34 = 12 \)
- \( 58 - 46 = 12 \)

### Step 2: Identify the pattern
The common difference between each pair of numbers is \( 12 \). This indicates that the sequence follows an **arithmetic progression** with a difference of \( 12 \).

### Step 3: Find the next number
To find the next number, we add \( 12 \) to the last term in the sequence:
\[
58 + 12 = 70
\]

Thus, the next number in the sequence is **70**.

---
Would you like further details or have any other questions?

Here are 5 related questions to expand on this:
1. What is an arithmetic progression, and how is it defined?
2. How would you find the general formula for the \(n\)-th term of this sequence?
3. Could this sequence have a quadratic or geometric pattern as well?
4. What is the sum of the first \(n\) terms in this arithmetic progression?
5. How do you differentiate between arithmetic and geometric sequences?

**Tip**: Always verify patterns by checking multiple consecutive terms for consistency!

Identify a pattern in the given list of numbers. Then use this pattern to find the next number. 10, 22, 34, 46, 58. The next number is

Learn how to identify a pattern in the sequence 10, 22, 34, 46, 58 and find the next number using arithmetic progression. This problem involves key mathematical concepts such as sequences and arithmetic progression, and is 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