The \[$ N \$\]th Term Of A Sequence Is Given By \[$\frac{n(n-8)}{\sqrt{n+3}}\$\].Work Out The Sum Of The 1st And 6th Terms. Your Final Line Must Say, Sum \[$ = \ldots \$\].

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The nth Term of a Sequence: Calculating the Sum of the 1st and 6th Terms

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. The nth term of a sequence is the term that appears at the nth position in the list. In this article, we will explore the nth term of a given sequence and calculate the sum of the 1st and 6th terms.

The nth Term of the Sequence

The nth term of the sequence is given by the formula:

n(n−8)n+3\frac{n(n-8)}{\sqrt{n+3}}

This formula represents the value of the nth term in the sequence. To calculate the sum of the 1st and 6th terms, we need to substitute n = 1 and n = 6 into the formula and then add the results.

Calculating the 1st Term

To calculate the 1st term, we substitute n = 1 into the formula:

1(1−8)1+3=1(−7)4=−72\frac{1(1-8)}{\sqrt{1+3}} = \frac{1(-7)}{\sqrt{4}} = \frac{-7}{2}

So, the 1st term of the sequence is -7/2.

Calculating the 6th Term

To calculate the 6th term, we substitute n = 6 into the formula:

6(6−8)6+3=6(−2)9=−123=−4\frac{6(6-8)}{\sqrt{6+3}} = \frac{6(-2)}{\sqrt{9}} = \frac{-12}{3} = -4

So, the 6th term of the sequence is -4.

Calculating the Sum of the 1st and 6th Terms

Now that we have calculated the 1st and 6th terms, we can add them together to find the sum:

−72+(−4)=−72−82=−152\frac{-7}{2} + (-4) = \frac{-7}{2} - \frac{8}{2} = \frac{-15}{2}

Therefore, the sum of the 1st and 6th terms of the sequence is -15/2.

In this article, we have explored the nth term of a given sequence and calculated the sum of the 1st and 6th terms. We have used the formula for the nth term to substitute n = 1 and n = 6 and then added the results to find the sum. The sum of the 1st and 6th terms is -15/2.

Sum = -15/2
The nth Term of a Sequence: Q&A

In our previous article, we explored the nth term of a given sequence and calculated the sum of the 1st and 6th terms. In this article, we will answer some frequently asked questions related to the nth term of a sequence.

Q: What is the nth term of a sequence?

A: The nth term of a sequence is the term that appears at the nth position in the list. It is a formula that represents the value of the nth term in the sequence.

Q: How do I calculate the nth term of a sequence?

A: To calculate the nth term of a sequence, you need to substitute the value of n into the formula for the nth term. For example, if the formula for the nth term is:

n(n−8)n+3\frac{n(n-8)}{\sqrt{n+3}}

You would substitute n = 1 to calculate the 1st term, n = 2 to calculate the 2nd term, and so on.

Q: What is the difference between the nth term and the general term of a sequence?

A: The nth term of a sequence is a specific term in the sequence, while the general term is a formula that represents the value of any term in the sequence. The general term is often used to describe the pattern of the sequence.

Q: How do I find the sum of the 1st and 6th terms of a sequence?

A: To find the sum of the 1st and 6th terms of a sequence, you need to calculate the 1st term and the 6th term separately and then add them together. For example, if the formula for the nth term is:

n(n−8)n+3\frac{n(n-8)}{\sqrt{n+3}}

You would substitute n = 1 to calculate the 1st term and n = 6 to calculate the 6th term, and then add the results together.

Q: What is the formula for the nth term of a sequence?

A: The formula for the nth term of a sequence is:

n(n−8)n+3\frac{n(n-8)}{\sqrt{n+3}}

This formula represents the value of the nth term in the sequence.

Q: Can I use the formula for the nth term to calculate any term in the sequence?

A: Yes, you can use the formula for the nth term to calculate any term in the sequence. Simply substitute the value of n into the formula to calculate the corresponding term.

Q: What if the formula for the nth term is not given? How do I find it?

A: If the formula for the nth term is not given, you may need to use other methods to find it. This can involve analyzing the pattern of the sequence, using algebraic manipulations, or using other mathematical techniques.

In this article, we have answered some frequently asked questions related to the nth term of a sequence. We have discussed how to calculate the nth term, how to find the sum of the 1st and 6th terms, and how to use the formula for the nth term to calculate any term in the sequence.

If you have any further questions or need help with a specific problem, feel free to ask.