Identify The Missing Number. 7629 = 7000 + … + 20 + 9 7629 = 7000 + \ldots + 20 + 9 7629 = 7000 + … + 20 + 9 A. 60 B. 660 C. 160 D. 600

Introduction

Mathematics is a fascinating subject that involves solving problems, identifying patterns, and making connections between different concepts. One of the fundamental aspects of mathematics is the concept of sequences and series, where numbers are arranged in a specific order to form a pattern. In this article, we will delve into the world of sequences and series, and explore a classic problem that requires the identification of a missing number.

The Problem

The problem we are about to discuss is a classic example of a sequence and series problem. It involves identifying a missing number in a sequence of numbers. The sequence is as follows:

$7629 = 7000 + \ldots + 20 + 9$

The problem asks us to identify the missing number in the sequence. The options provided are:

A. 60 B. 660 C. 160 D. 600

Understanding the Sequence

To solve this problem, we need to understand the pattern of the sequence. The sequence starts with the number 7000 and ends with the number 9. The numbers in the sequence are arranged in a specific order, with each number being smaller than the previous one. This is a classic example of an arithmetic sequence, where each term is obtained by adding a fixed constant to the previous term.

Identifying the Pattern

To identify the missing number, we need to analyze the pattern of the sequence. Let's take a closer look at the sequence:

$7000, 6900, 6800, 6700, 6600, 6500, 6400, 6300, 6200, 6100, 6000, 5900, 5800, 5700, 5600, 5500, 5400, 5300, 5200, 5100, 5000, 4900, 4800, 4700, 4600, 4500, 4400, 4300, 4200, 4100, 4000, 3900, 3800, 3700, 3600, 3500, 3400, 3300, 3200, 3100, 3000, 2900, 2800, 2700, 2600, 2500, 2400, 2300, 2200, 2100, 2000, 1900, 1800, 1700, 1600, 1500, 1400, 1300, 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 9$

As we can see, the sequence is an arithmetic sequence with a common difference of -100. This means that each term is obtained by subtracting 100 from the previous term.

Solving the Problem

Now that we have identified the pattern of the sequence, we can solve the problem. The sequence starts with the number 7000 and ends with the number 9. The missing number is the one that is missing in the sequence. To find the missing number, we need to find the term that is missing in the sequence.

Let's analyze the sequence again:

$7000, 6900, 6800, 6700, 6600, 6500, 6400, 6300, 6200, 6100, 6000, 5900, 5800, 5700, 5600, 5500, 5400, 5300, 5200, 5100, 5000, 4900, 4800, 4700, 4600, 4500, 4400, 4300, 4200, 4100, 4000, 3900, 3800, 3700, 3600, 3500, 3400, 3300, 3200, 3100, 3000, 2900, 2800, 2700, 2600, 2500, 2400, 2300, 2200, 2100, 2000, 1900, 1800, 1700, 1600, 1500, 1400, 1300, 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 90, 80, 70, 60, 50, 40, 30, 20, 9$

As we can see, the sequence is missing the number 60. Therefore, the correct answer is:

A. 60

Conclusion

In this article, we have discussed a classic problem of identifying a missing number in a sequence. We have analyzed the pattern of the sequence and identified the missing number. The correct answer is A. 60. This problem requires a deep understanding of sequences and series, and it is a great example of how mathematics can be used to solve real-world problems.

Real-World Applications

The concept of sequences and series has many real-world applications. For example, in finance, sequences and series are used to calculate interest rates and investments. In engineering, sequences and series are used to design and analyze complex systems. In computer science, sequences and series are used to develop algorithms and data structures.

Final Thoughts

In conclusion, the problem of identifying a missing number in a sequence is a classic example of a sequence and series problem. It requires a deep understanding of the pattern of the sequence and the ability to analyze and solve the problem. This problem has many real-world applications and is a great example of how mathematics can be used to solve real-world problems.

References

• [1] "Sequences and Series" by Math Open Reference
• [2] "Arithmetic Sequences and Series" by Khan Academy
• [3] "Sequences and Series" by Wolfram MathWorld

Additional Resources

• [1] "Sequences and Series" by MIT OpenCourseWare
• [2] "Arithmetic Sequences and Series" by Purplemath
• [3] "Sequences and Series" by Mathway

Glossary

• Arithmetic Sequence: A sequence of numbers in which each term is obtained by adding a fixed constant to the previous term.
• Common Difference: The fixed constant that is added to each term in an arithmetic sequence.
• Sequence: A list of numbers in a specific order.
• Series: The sum of a sequence of numbers.
  Q&A: Identifying Missing Numbers in Sequences =====================================================

Introduction

In our previous article, we discussed a classic problem of identifying a missing number in a sequence. We analyzed the pattern of the sequence and identified the missing number. In this article, we will provide a Q&A section to help you better understand the concept of sequences and series, and how to identify missing numbers in sequences.

Q1: What is a sequence?

A sequence is a list of numbers in a specific order. It can be a finite or infinite list of numbers, and it can be arranged in any order.

A1: A sequence can be a list of numbers in any order, such as 1, 2, 3, 4, 5 or 5, 4, 3, 2, 1.

Q2: What is a series?

A series is the sum of a sequence of numbers. It is the result of adding up all the numbers in a sequence.

A2: For example, if we have a sequence of numbers 1, 2, 3, 4, 5, the series would be 1 + 2 + 3 + 4 + 5 = 15.

Q3: What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term is obtained by adding a fixed constant to the previous term.

A3: For example, if we have an arithmetic sequence with a common difference of 2, the sequence would be 1, 3, 5, 7, 9.

Q4: How do I identify a missing number in a sequence?

To identify a missing number in a sequence, you need to analyze the pattern of the sequence and determine the next number in the sequence.

A4: For example, if we have a sequence of numbers 2, 4, 6, 8, 10, the next number in the sequence would be 12.

Q5: What is the common difference in an arithmetic sequence?

The common difference in an arithmetic sequence is the fixed constant that is added to each term to obtain the next term.

A5: For example, if we have an arithmetic sequence with a common difference of 2, the sequence would be 1, 3, 5, 7, 9.

Q6: How do I determine the next number in an arithmetic sequence?

To determine the next number in an arithmetic sequence, you need to add the common difference to the previous term.

A6: For example, if we have an arithmetic sequence with a common difference of 2 and the previous term is 5, the next number in the sequence would be 5 + 2 = 7.

Q7: What is the formula for the nth term of an arithmetic sequence?

The formula for the nth term of an arithmetic sequence is:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the term number, and d is the common difference.

A7: For example, if we have an arithmetic sequence with a first term of 2 and a common difference of 3, the formula for the nth term would be:

an = 2 + (n - 1)3

Q8: How do I use the formula to find the nth term of an arithmetic sequence?

To use the formula to find the nth term of an arithmetic sequence, you need to plug in the values of a1, n, and d into the formula.

A8: For example, if we have an arithmetic sequence with a first term of 2, a term number of 5, and a common difference of 3, the formula would be:

an = 2 + (5 - 1)3 an = 2 + 4(3) an = 2 + 12 an = 14

Conclusion

In this Q&A article, we have discussed the concept of sequences and series, and how to identify missing numbers in sequences. We have also provided formulas and examples to help you better understand the concept. We hope this article has been helpful in your understanding of sequences and series.

Additional Resources

• [1] "Sequences and Series" by MIT OpenCourseWare
• [2] "Arithmetic Sequences and Series" by Purplemath
• [3] "Sequences and Series" by Mathway

Glossary

• Arithmetic Sequence: A sequence of numbers in which each term is obtained by adding a fixed constant to the previous term.
• Common Difference: The fixed constant that is added to each term in an arithmetic sequence.
• Sequence: A list of numbers in a specific order.
• Series: The sum of a sequence of numbers.