key term - First Term

Definition

The first term in a sequence is the initial value or starting point of the sequence. It establishes the foundation upon which the subsequent terms in the sequence are built.

5 Must Know Facts For Your Next Test

1. The first term of an arithmetic sequence is the starting point or initial value of the sequence.
2. The first term, along with the common difference, determines the entire sequence.
3. Identifying the first term is crucial for understanding and working with arithmetic sequences.
4. The first term can be a positive, negative, or zero value, depending on the context of the sequence.
5. Knowing the first term allows you to predict and calculate any subsequent term in the sequence.

Review Questions

• Explain the importance of the first term in an arithmetic sequence.
  • The first term in an arithmetic sequence is essential because it establishes the starting point of the sequence. Along with the common difference, the first term determines the entire sequence and allows you to predict and calculate any subsequent term. Identifying the first term is a crucial step in understanding and working with arithmetic sequences, as it provides the foundation upon which the pattern is built.
• Describe how the first term and common difference work together to define an arithmetic sequence.
  • The first term and common difference work together to define an arithmetic sequence. The first term provides the initial value or starting point of the sequence, while the common difference is the constant value that is added to each term to generate the next term. By knowing the first term and the common difference, you can generate the entire sequence by repeatedly adding the common difference to the previous term. This relationship between the first term and common difference is fundamental to understanding and working with arithmetic sequences.
• Analyze the role of the first term in predicting and calculating subsequent terms in an arithmetic sequence.
  • The first term plays a crucial role in predicting and calculating subsequent terms in an arithmetic sequence. Since the sequence follows a specific pattern where each term is obtained by adding the common difference to the previous term, the first term serves as the foundation for this pattern. By knowing the first term and the common difference, you can use the formula $a_n = a_1 + (n-1)d$ to determine any term in the sequence, where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference. This allows you to accurately predict and calculate the values of subsequent terms in the sequence, making the first term an essential component in understanding and working with arithmetic sequences.

Related terms

Sequence:

A sequence is an ordered list of numbers, objects, or other elements that follow a specific pattern or rule.

Common Difference:

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

Arithmetic Progression:

An arithmetic progression is a sequence where the difference between any two consecutive terms is constant.