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Chapter 11: Problem 12

Solve. See Example 2. Find the sum of the first five negative odd integers.

Short Answer

Expert verified
The sum of the first five negative odd integers is -25.

Step by step solution

01

Identify the Sequence

First, list the first five negative odd integers. These are -1, -3, -5, -7, and -9. These are the numbers that we need to add together.
02

Write the Addition Problem

Set up the addition of these five numbers explicitly: (-1) + (-3) + (-5) + (-7) + (-9).
03

Add the Numbers

Perform the addition step by step: 1. (-1) + (-3) = -4 2. (-4) + (-5) = -9 3. (-9) + (-7) = -16 4. (-16) + (-9) = -25
04

Confirm the Result

Check each step to confirm that the addition was done correctly, ensuring that you correctly accounted for the signs of each number.

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Key Concepts

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

Odd Integers
When we talk about odd integers, we are referring to numbers that cannot be exactly divided by 2.
Imagine numbers on a number line, where odd integers are spaced evenly apart, with even numbers in between.
This means numbers like -1, -3, -5, and so on, are odd integers. Odd integers are essential because they form part of integer sequences, which is a key concept in mathematics.
In the context of negative numbers, they still follow the same rule: their division by 2 will leave a remainder.
  • Odd integers always end with 1, 3, 5, 7, or 9.
  • Negative odd integers simply mirror the positive ones but in the negative space.
Integer Sequence
An integer sequence is a list of integers arranged in a specific order.
Each number, or term, in the sequence must follow a particular pattern or rule.
For example, the sequence of negative odd integers is -1, -3, -5, -7, -9, etc. These sequences are useful because they help us understand patterns in numbers, making complex problems more manageable.
A sequence allows us to predict subsequent terms based on their observed pattern.
  • Each term in the negative odd integer sequence decreases by 2 from the previous term.
  • The sequence is infinitely long, both in positive and negative directions.
Addition of Integers
Adding integers involves combining numbers to find their total value.
This can involve positive and negative numbers. In our exercise, we focused on adding negative odd integers. The process is simple: align them in an addition problem, then proceed step by step.
  • The trickiest part is keeping track of the negative signs, as they change the direction of the number's value on the number line.
  • When adding two negative numbers, the result is a more negative number.
Arithmetic Operations
In mathematics, arithmetic operations are the basic calculations we perform: addition, subtraction, multiplication, and division.
In this example, we focused on addition, which is the process of finding the sum of two or more numbers. Arithmetic is the foundation of many areas in math.
Understanding arithmetic operations, especially with negative integers, is crucial, as it helps solve more complex problems later on.
  • When performing arithmetic operations with negative numbers, always consider their signs.
  • Each operation follows specific rules that help maintain consistent results across problems.

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Most popular questions from this chapter

Solve. Find the sum of the first five terms of the sequence \(-2,-6\) \(-18, \ldots\)

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