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Chapter 2: Problem 75

Write the next three numbers in the sequence. 5,1,-3,-7, __, __, __.

Short Answer

Expert verified
The next three numbers in the sequence are -11, -15, -19.

Step by step solution

01

Identify the pattern

Look for a pattern in the changes between consecutive numbers in the sequence. Here, we see that each number is 4 less than the previous number.
02

Apply the pattern to find the next number

Subtract 4 from the last number in the sequence: -7 - 4 = -11
03

Continue applying the pattern

Keep subtracting 4 to find the next number: -11 - 4 = -15
04

Find the final number

Subtract 4 one last time to get the third number: -15 - 4 = -19

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Key Concepts

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

number patterns
Number patterns are sequences of numbers that follow a particular rule. By observing the pattern, you can predict the following numbers. In this exercise, the sequence follows a consistent change: each number is 4 less than the previous one. Identifying such a pattern is crucial for solving number sequence problems. Recognizing these patterns helps in various math problems and strengthens problem-solving skills.
subtraction
Subtraction is the process of taking one number away from another. It is essential for identifying sequences like the one given: 5, 1, -3, -7. We find the next numbers by subtracting 4 repeatedly. Performing subtraction with negative numbers can be tricky, but practicing it will make you confident. For instance, from -7, subtracting 4 gets you -11. This process helps in understanding number flow and changes.
sequence and series
A sequence is a list of numbers arranged in a specific order. When we add the numbers, it forms a series. Sequences can increase or decrease based on a rule. Understanding sequences involves recognizing the pattern and predicting the next terms. In our example, the sequence decreases by 4 each time. Real-life examples include the days of the week, where the pattern follows a 7-day repeat.
negative numbers
Negative numbers are values less than zero. They are vital in arithmetic sequences progressing into negative values. In the problem, the sequence becomes more negative with each step. Handling negative numbers in subtraction is fundamental. For instance, you start with -7, and subtracting 4 makes it -11. Practicing with negative numbers will make you proficient in tackling more complex sequences.

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Most popular questions from this chapter

Translate each English phrase to a mathematical expression. Then simplify. Subtract 10 from 16

Perform the indicated operation. $$(-9)(-12)$$

Find the range. The range of a set of numbers is the difference between the highest value and the lowest value. That is, range = highest - lowest. Find two integers whose difference is \(-20 .\) Answers may vary.

Perform the indicated operation. $$\frac{0}{-5}$$

Perform the indicated operation. $$(-2)(-5)(4)$$
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