The first term of a finite arithmetic sequence is called the first term, and the last term is called the last term.
Here's a more detailed look at arithmetic sequences:
Understanding Arithmetic Sequences
An arithmetic sequence is a series of numbers where the difference between any two consecutive terms is constant. This constant difference is known as the common difference.
- First Term (a): This is the starting number of the sequence. In the context of formulas, it's often denoted as 'a'.
- Common Difference (d): The value that is added to each term to get the next.
- Number of Terms (n): The total count of terms in the sequence.
- Last Term (an): This is the final number in a finite arithmetic sequence, and it is often denoted by 'an'.
Key Components of a Finite Arithmetic Sequence
| Term | Description | Notation |
|---|---|---|
| First Term | The initial number of the arithmetic sequence | a |
| Common Difference | The constant value added to each term to get the next term | d |
| Number of Terms | The total count of numbers within the arithmetic sequence. The number of terms is always a positive integer | n |
| Last Term | The final number in the arithmetic sequence | an |
Example of an Arithmetic Sequence
Let's look at the sequence: 2, 5, 8, 11, 14.
- First Term (a): 2
- Common Difference (d): 3 (since 5-2=3, 8-5=3, etc.)
- Number of Terms (n): 5
- Last Term (an): 14
Therefore, in this example, '2' is the first term, and '14' is the last term.
In summary, the first term of an arithmetic sequence is always the first number in the sequence, and the last term is the final number when dealing with a finite sequence. These terms, along with the common difference and the number of terms, define the characteristics of an arithmetic sequence.
