The N N N Th Term Of A Sequence Is 3 N + 2 3n + 2 3 N + 2 .a) Work Out The First Three Terms Of The Sequence. □ \square □ □ \square □ □ \square □ B) Work Out The Tenth Term Of The Sequence. □ \square □

Introduction

In mathematics, sequences are an essential concept that helps us understand patterns and relationships between numbers. A sequence is a list of numbers in a specific order, and each number in the list is called a term. In this article, we will explore the nth term of a sequence, which is given by the formula $3n + 2$. We will work out the first three terms of the sequence and the tenth term, and discuss the pattern that emerges.

The Formula for the nth Term

The formula for the nth term of the sequence is $3n + 2$. This means that to find the nth term, we need to multiply the value of n by 3 and then add 2.

Working Out the First Three Terms

To work out the first three terms of the sequence, we need to substitute the values of n into the formula.

• For the first term (n = 1), we substitute n = 1 into the formula: $3(1) + 2 = 3 + 2 = 5$. So, the first term of the sequence is 5.
• For the second term (n = 2), we substitute n = 2 into the formula: $3(2) + 2 = 6 + 2 = 8$. So, the second term of the sequence is 8.
• For the third term (n = 3), we substitute n = 3 into the formula: $3(3) + 2 = 9 + 2 = 11$. So, the third term of the sequence is 11.

The First Three Terms of the Sequence

The first three terms of the sequence are 5, 8, and 11.

Working Out the Tenth Term

To work out the tenth term of the sequence, we need to substitute n = 10 into the formula.

• For the tenth term (n = 10), we substitute n = 10 into the formula: $3(10) + 2 = 30 + 2 = 32$. So, the tenth term of the sequence is 32.

The Tenth Term of the Sequence

The tenth term of the sequence is 32.

Understanding the Pattern

As we can see from the first three terms of the sequence (5, 8, 11), the pattern is that each term is increasing by 3. This is because the formula for the nth term is $3n + 2$, and when we substitute the values of n into the formula, we get a sequence of numbers that are increasing by 3.

Conclusion

In conclusion, the nth term of a sequence is given by the formula $3n + 2$. We worked out the first three terms of the sequence and the tenth term, and discussed the pattern that emerges. The pattern is that each term is increasing by 3, and this is due to the formula for the nth term. Understanding the pattern of a sequence is essential in mathematics, and it helps us to make predictions and generalizations about the behavior of the sequence.

Applications of the nth Term Formula

The nth term formula has many applications in mathematics and other fields. For example, it can be used to model population growth, financial investments, and other real-world phenomena. It can also be used to solve problems in algebra, geometry, and calculus.

Real-World Examples

Here are a few real-world examples of how the nth term formula can be used:

• Population Growth: Suppose a city has a population of 100,000 people, and it is growing at a rate of 3% per year. We can use the nth term formula to model the population growth over time.
• Financial Investments: Suppose you invest $1,000 in a savings account that earns a 5% interest rate per year. We can use the nth term formula to calculate the future value of the investment.
• Geometry: Suppose we have a geometric sequence of numbers, where each term is obtained by multiplying the previous term by a fixed constant. We can use the nth term formula to find the nth term of the sequence.

Conclusion

Introduction

In our previous article, we explored the nth term of a sequence, which is given by the formula $3n + 2$. We worked out the first three terms of the sequence and the tenth term, and discussed the pattern that emerges. In this article, we will answer some frequently asked questions about the nth term formula and its applications.

Q: What is the nth term formula?

A: The nth term formula is a mathematical formula that gives the nth term of a sequence. It is given by the formula $3n + 2$, where n is the term number.

Q: How do I use the nth term formula?

A: To use the nth term formula, simply substitute the value of n into the formula. For example, to find the 5th term of the sequence, substitute n = 5 into the formula: $3(5) + 2 = 15 + 2 = 17$.

Q: What is the pattern of the sequence?

A: The pattern of the sequence is that each term is increasing by 3. This is because the formula for the nth term is $3n + 2$, and when we substitute the values of n into the formula, we get a sequence of numbers that are increasing by 3.

Q: Can I use the nth term formula to model real-world phenomena?

A: Yes, the nth term formula can be used to model a wide range of real-world phenomena, including population growth, financial investments, and geometric sequences.

Q: How do I apply the nth term formula to a real-world problem?

A: To apply the nth term formula to a real-world problem, simply identify the pattern of the sequence and use the formula to model the behavior of the sequence. For example, if you are modeling population growth, use the nth term formula to calculate the population at each time period.

Q: What are some common applications of the nth term formula?

A: Some common applications of the nth term formula include:

• Population Growth: Use the nth term formula to model population growth over time.
• Financial Investments: Use the nth term formula to calculate the future value of an investment.
• Geometry: Use the nth term formula to find the nth term of a geometric sequence.
• Algebra: Use the nth term formula to solve problems in algebra, such as finding the value of a variable.

Q: Can I use the nth term formula to solve problems in calculus?

A: Yes, the nth term formula can be used to solve problems in calculus, such as finding the derivative of a function.

Q: What are some common mistakes to avoid when using the nth term formula?

A: Some common mistakes to avoid when using the nth term formula include:

• Not substituting the correct value of n: Make sure to substitute the correct value of n into the formula.
• Not using the correct formula: Make sure to use the correct formula for the nth term.
• Not checking the units: Make sure to check the units of the answer to ensure that it is correct.

Conclusion

In conclusion, the nth term formula is a powerful tool in mathematics that can be used to model and analyze a wide range of phenomena. It has many applications in mathematics and other fields, and it can be used to solve problems in algebra, geometry, and calculus. By understanding the pattern of a sequence and using the nth term formula, you can make predictions and generalizations about the behavior of the sequence.