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Chapter 2: Problem 55

If \(n\) represents an odd number, what is the next larger odd number?

Short Answer

Expert verified
The next larger odd number is \(n + 2\).

Step by step solution

01

Identify the Pattern

Odd numbers are numbers that cannot be evenly divided by 2. They follow a sequence such as 1, 3, 5, 7, etc., where each odd number is followed by another odd number.
02

Determine the Next Odd Number

If you have an odd number, the next number in the sequence that is also odd can be found by adding 2 to it. This is because adding 1 would give you an even number, and we need to ensure the sum results in another odd number.
03

Symbolically Represent

Given an odd number \(n\), the next odd number is \(n + 2\). This formula can be used universally to find the next number in the sequence of odd numbers.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Number sequence
Number sequences are fascinating as they help us identify patterns in numbers. Odd numbers are a specific type of sequence where each follows a regular pattern. By recognizing this pattern, we can predict the continuation of the sequence easily.
  • An odd number is one that leaves a remainder when divided by 2. For instance, 1, 3, 5, and 7 are odd numbers.
  • In a sequence of odd numbers, each number is consistently 2 more than the preceding odd number. This regular increase ensures the sequence continues smoothly without any gaps.
A sequence like 1, 3, 5, 7, etc., illustrates this pattern clearly. Understanding number sequences allows us to predict upcoming numbers, solve mathematical problems, and recognize relationships between numbers.
Algebraic expressions
Algebraic expressions allow us to capture patterns in a formulaic way. When dealing with sequences, such as odd numbers, we often use algebra to express them.
  • In algebra, an odd number can be expressed as \( n \), where \( n \) itself signifies any odd number. It's an abstract representation that simplifies calculations.
  • The next odd number in sequence can be represented by the expression \( n + 2 \). This algebraic expression is derived from the pattern that each subsequent odd number is 2 units away from its predecessor.
Using algebraic expressions like these, we can generalize and solve complex problems efficiently. They serve as tools to work through various math scenarios seamlessly.
Arithmetic operations
Arithmetic operations are fundamental building blocks in mathematics, enabling us to manipulate numbers in meaningful ways. To navigate from one odd number to the next, we rely on these operations.
  • The addition operation allows us to move through the odd number sequence. By adding 2, we shift from one odd number to the next.
  • Attempts to add 1 would lead us to an even number, disrupting the odd sequence, reinforcing the role of specific arithmetic operations for particular sequences.
Understanding how arithmetic operations function aids not only in tackling specific problems but also in developing a broader comprehension of mathematical rules and relationships.

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Most popular questions from this chapter

Simplify each algebraic expression by combinang similar terms. $$\frac{2}{9} x+\frac{5}{12} y-\frac{7}{15} x-\frac{13}{15} y$$

Give a step-by-step description of the best way to add the rational numbers \(\frac{3}{8}\) and \(\frac{5}{18}\).

Simplify each of the numerical expressions. $$5(2.3)-1.2-7.36 \div 0.8+0.2$$

Simplify each of the numerical expressions. $$(0.96) \div(-0.8)+6(-1.4)-5.2$$

Simplify each of the numerical expressions. $$7(0.6)+0.9-3(0.4)+0.4$$
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