Match The Parts Of The Following Function With Their Correct Definitions.$A(n)=a+(n-1) D$1. D D D - Common Difference 2. A A A - Value Of The First Term 3. A ( N A(n A ( N ] - Value Of The Nth Term 4. N N N - Number Of

In mathematics, an arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is known as the common difference. The arithmetic sequence function is a mathematical representation of this sequence, and it is used to find the value of any term in the sequence. In this article, we will match the parts of the arithmetic sequence function with their correct definitions.

The Arithmetic Sequence Function

The arithmetic sequence function is given by the formula:

$$A(n) = a + (n-1)d$$

where $A(n)$ is the value of the nth term, $a$ is the value of the first term, $d$ is the common difference, and $n$ is the number of terms.

Matching the Parts of the Function

Now, let's match the parts of the function with their correct definitions.

1. $d$ - Common Difference

The common difference is the constant difference between any two consecutive terms in an arithmetic sequence. It is denoted by the symbol $d$. The common difference is the key to finding the value of any term in the sequence.

For example, in the sequence 2, 5, 8, 11, 14, the common difference is 3, because each term is obtained by adding 3 to the previous term.

2. $a$ - Value of the First Term

The value of the first term is the first term in the sequence. It is denoted by the symbol $a$. The value of the first term is the starting point of the sequence, and it is used as the base to find the value of any other term.

For example, in the sequence 2, 5, 8, 11, 14, the value of the first term is 2.

3. $A(n)$ - Value of the nth Term

The value of the nth term is the value of the nth term in the sequence. It is denoted by the symbol $A(n)$. The value of the nth term is found by using the formula $A(n) = a + (n-1)d$, where $a$ is the value of the first term, $d$ is the common difference, and $n$ is the number of terms.

For example, in the sequence 2, 5, 8, 11, 14, the value of the 5th term is 14, which is found by using the formula $A(5) = 2 + (5-1)3$.

4. $n$ - Number of Terms

The number of terms is the total number of terms in the sequence. It is denoted by the symbol $n$. The number of terms is used to find the value of any term in the sequence.

For example, in the sequence 2, 5, 8, 11, 14, the number of terms is 5.

Example Problems

Now that we have matched the parts of the function with their correct definitions, let's solve some example problems.

Example 1

Find the value of the 10th term in the sequence 3, 6, 9, 12, 15, ...

We know that the value of the first term is 3, the common difference is 3, and the number of terms is 10. Using the formula $A(n) = a + (n-1)d$, we can find the value of the 10th term:

$$A(10) = 3 + (10-1)3$$

$$A(10) = 3 + 9(3)$$

$$A(10) = 3 + 27$$

$$A(10) = 30$$

Therefore, the value of the 10th term is 30.

Example 2

Find the common difference in the sequence 1, 4, 7, 10, 13, ...

We know that the value of the first term is 1, the value of the 5th term is 13, and the number of terms is 5. Using the formula $A(n) = a + (n-1)d$, we can find the common difference:

$$13 = 1 + (5-1)d$$

$$13 = 1 + 4d$$

$$12 = 4d$$

$$d = 3$$

Therefore, the common difference is 3.

Conclusion

In this article, we have matched the parts of the arithmetic sequence function with their correct definitions. We have also solved some example problems to illustrate how to use the formula to find the value of any term in the sequence. The arithmetic sequence function is a powerful tool in mathematics, and it is used to find the value of any term in an arithmetic sequence.

References

• [1] "Arithmetic Sequence" by Math Open Reference. Retrieved from https://www.mathopenref.com/arithmeticsequence.html
• [2] "Arithmetic Sequence Formula" by Mathway. Retrieved from https://www.mathway.com/sequences/arithmetic-sequence-formula

Glossary

• Arithmetic Sequence: A sequence of numbers in which the difference between any two consecutive terms is constant.
• Common Difference: The constant difference between any two consecutive terms in an arithmetic sequence.
• Value of the First Term: The first term in the sequence.
• Value of the nth Term: The value of the nth term in the sequence.
• Number of Terms: The total number of terms in the sequence.
  Arithmetic Sequence Function Q&A =====================================

In the previous article, we discussed the arithmetic sequence function and matched its parts with their correct definitions. In this article, we will answer some frequently asked questions about the arithmetic sequence function.

Q: What is the arithmetic sequence function?

A: The arithmetic sequence function is a mathematical representation of an arithmetic sequence. It is used to find the value of any term in the sequence.

Q: What is the formula for the arithmetic sequence function?

A: The formula for the arithmetic sequence function is:

$$A(n) = a + (n-1)d$$

where $A(n)$ is the value of the nth term, $a$ is the value of the first term, $d$ is the common difference, and $n$ is the number of terms.

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

A: The common difference is the constant difference between any two consecutive terms in an arithmetic sequence. It is denoted by the symbol $d$.

Q: How do I find the common difference in an arithmetic sequence?

A: To find the common difference in an arithmetic sequence, you can use the formula:

$$d = \frac{A(n) - A(n-1)}{1}$$

where $A(n)$ is the value of the nth term and $A(n-1)$ is the value of the (n-1)th term.

Q: What is the value of the first term in an arithmetic sequence?

A: The value of the first term is the first term in the sequence. It is denoted by the symbol $a$.

Q: How do I find the value of the first term in an arithmetic sequence?

A: To find the value of the first term in an arithmetic sequence, you can use the formula:

$$a = A(1)$$

where $A(1)$ is the value of the first term.

Q: What is the value of the nth term in an arithmetic sequence?

A: The value of the nth term is the value of the nth term in the sequence. It is denoted by the symbol $A(n)$.

Q: How do I find the value of the nth term in an arithmetic sequence?

A: To find the value of the nth term in an arithmetic sequence, you can use the formula:

$$A(n) = a + (n-1)d$$

where $a$ is the value of the first term, $d$ is the common difference, and $n$ is the number of terms.

Q: What is the number of terms in an arithmetic sequence?

A: The number of terms is the total number of terms in the sequence. It is denoted by the symbol $n$.

Q: How do I find the number of terms in an arithmetic sequence?

A: To find the number of terms in an arithmetic sequence, you can use the formula:

$$n = \frac{A(n) - a}{d} + 1$$

where $A(n)$ is the value of the nth term, $a$ is the value of the first term, and $d$ is the common difference.

Q: Can I use the arithmetic sequence function to find the value of any term in a geometric sequence?

A: No, the arithmetic sequence function is used to find the value of any term in an arithmetic sequence, not a geometric sequence. A geometric sequence is a sequence of numbers in which the ratio between any two consecutive terms is constant.

Q: Can I use the arithmetic sequence function to find the value of any term in a mixed sequence?

A: No, the arithmetic sequence function is used to find the value of any term in an arithmetic sequence, not a mixed sequence. A mixed sequence is a sequence of numbers that contains both arithmetic and geometric terms.

Conclusion

In this article, we have answered some frequently asked questions about the arithmetic sequence function. We have also provided formulas and examples to help you understand how to use the arithmetic sequence function to find the value of any term in an arithmetic sequence.

References

• [1] "Arithmetic Sequence" by Math Open Reference. Retrieved from https://www.mathopenref.com/arithmeticsequence.html
• [2] "Arithmetic Sequence Formula" by Mathway. Retrieved from https://www.mathway.com/sequences/arithmetic-sequence-formula

Glossary

• Arithmetic Sequence: A sequence of numbers in which the difference between any two consecutive terms is constant.
• Common Difference: The constant difference between any two consecutive terms in an arithmetic sequence.
• Value of the First Term: The first term in the sequence.
• Value of the nth Term: The value of the nth term in the sequence.
• Number of Terms: The total number of terms in the sequence.