Working Out the First Three Terms

Oct 13, 2025 by talynt.org 23 views

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Introduction

In mathematics, a sequence is a list of numbers in a specific order. Sequences can be defined by a formula, and the nth term of a sequence is the term that corresponds to the nth position in the sequence. In this article, we will explore the concept of the nth term of a sequence and work out the first three terms of a given sequence.

What is the nth Term of a Sequence?

The nth term of a sequence is the term that corresponds to the nth position in the sequence. It is usually denoted by the formula a_n, where n is the position of the term. For example, if we have a sequence a_1, a_2, a_3, ..., then the nth term of the sequence is a_n.

The Given Sequence

The given sequence is defined by the formula 30 - 2n. This means that the nth term of the sequence is 30 - 2n.

Working Out the First Three Terms

To work out the first three terms of the sequence, we need to substitute n with the values 1, 2, and 3 in the formula 30 - 2n.

First Term

For the first term, we substitute n with 1 in the formula 30 - 2n. This gives us:

30 - 2(1) = 30 - 2 = 28

So, the first term of the sequence is 28.

Second Term

For the second term, we substitute n with 2 in the formula 30 - 2n. This gives us:

30 - 2(2) = 30 - 4 = 26

So, the second term of the sequence is 26.

Third Term

For the third term, we substitute n with 3 in the formula 30 - 2n. This gives us:

30 - 2(3) = 30 - 6 = 24

So, the third term of the sequence is 24.

Conclusion

In this article, we have worked out the first three terms of a given sequence defined by the formula 30 - 2n. We have shown that the first term is 28, the second term is 26, and the third term is 24. This demonstrates the concept of the nth term of a sequence and how to work out the terms of a sequence using a formula.

Frequently Asked Questions

Q: What is the nth term of a sequence?

A: The nth term of a sequence is the term that corresponds to the nth position in the sequence.

Q: How do I work out the terms of a sequence?

A: To work out the terms of a sequence, you need to substitute the value of n in the formula that defines the sequence.

Q: What is the formula for the given sequence?

A: The formula for the given sequence is 30 - 2n.

References

Glossary

Sequence: A list of numbers in a specific order.
Nth term: The term that corresponds to the nth position in the sequence.
Formula: A mathematical expression that defines a sequence.
Term: A single number in a sequence.

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Introduction

In our previous article, we explored the concept of the nth term of a sequence and worked out the first three terms of a given sequence. In this article, we will answer some frequently asked questions about the nth term of a sequence.

Q&A

Q: What is the nth term of a sequence?

A: The nth term of a sequence is the term that corresponds to the nth position in the sequence. It is usually denoted by the formula a_n, where n is the position of the term.

Q: How do I work out the terms of a sequence?

A: To work out the terms of a sequence, you need to substitute the value of n in the formula that defines the sequence. For example, if the formula is a_n = 2n + 1, then you can work out the first few terms by substituting n with the values 1, 2, 3, etc.

Q: What is the formula for the given sequence?

A: The formula for the given sequence is 30 - 2n. This means that the nth term of the sequence is 30 - 2n.

Q: How do I know which term is which?

A: To know which term is which, you need to substitute the value of n in the formula that defines the sequence. For example, if the formula is a_n = 2n + 1, then the first term is a_1 = 2(1) + 1 = 3, the second term is a_2 = 2(2) + 1 = 5, and so on.

Q: Can I use the nth term of a sequence to find the sum of the sequence?

A: Yes, you can use the nth term of a sequence to find the sum of the sequence. However, you need to know the number of terms in the sequence and the formula that defines the sequence.

Q: How do I find the sum of the first n terms of a sequence?

A: To find the sum of the first n terms of a sequence, you need to use the formula for the sum of a sequence. The formula is S_n = a_1 + a_2 + ... + a_n, where S_n is the sum of the first n terms and a_1, a_2, etc. are the terms of the sequence.

Q: Can I use the nth term of a sequence to find the product of the sequence?

A: Yes, you can use the nth term of a sequence to find the product of the sequence. However, you need to know the number of terms in the sequence and the formula that defines the sequence.

Q: How do I find the product of the first n terms of a sequence?

A: To find the product of the first n terms of a sequence, you need to use the formula for the product of a sequence. The formula is P_n = a_1 * a_2 * ... * a_n, where P_n is the product of the first n terms and a_1, a_2, etc. are the terms of the sequence.

Conclusion

In this article, we have answered some frequently asked questions about the nth term of a sequence. We have shown that the nth term of a sequence is the term that corresponds to the nth position in the sequence and that you can use the formula that defines the sequence to work out the terms of the sequence.

References

Glossary

Sequence: A list of numbers in a specific order.
Nth term: The term that corresponds to the nth position in the sequence.
Formula: A mathematical expression that defines a sequence.
Term: A single number in a sequence.
Sum: The total of a sequence of numbers.
Product: The result of multiplying a sequence of numbers together.