Question
What is the sequence for ((an = a1 + (n - 1)d)
Answers
GPT-4o mini
The expression you've provided is the formula for the n-th term of an arithmetic sequence. In this formula:
- \( a_n \) is the n-th term of the sequence.
- \( a_1 \) is the first term of the sequence.
- \( n \) is the term number (a positive integer).
- \( d \) is the common difference between consecutive terms in the sequence.
The sequence itself can be generated by starting from the first term \( a_1 \) and repeatedly adding the common difference \( d \).
For example, if we have \( a_1 = 2 \) and \( d = 3 \):
- The first term (\( a_1 \)) is \( 2 \).
- The second term (\( a_2 \)) is \( a_1 + d = 2 + 3 = 5 \).
- The third term (\( a_3 \)) is \( a_1 + 2d = 2 + 2 \times 3 = 8 \).
- The fourth term (\( a_4 \)) is \( a_1 + 3d = 2 + 3 \times 3 = 11 \).
So the sequence would be: \( 2, 5, 8, 11, \ldots \).
In general, the sequence can be written as:
\[ a_1, a_1 + d, a_1 + 2d, a_1 + 3d, \ldots \]
If you have specific values for \( a_1 \) and \( d \), you can generate the terms of the sequence accordingly!
- \( a_n \) is the n-th term of the sequence.
- \( a_1 \) is the first term of the sequence.
- \( n \) is the term number (a positive integer).
- \( d \) is the common difference between consecutive terms in the sequence.
The sequence itself can be generated by starting from the first term \( a_1 \) and repeatedly adding the common difference \( d \).
For example, if we have \( a_1 = 2 \) and \( d = 3 \):
- The first term (\( a_1 \)) is \( 2 \).
- The second term (\( a_2 \)) is \( a_1 + d = 2 + 3 = 5 \).
- The third term (\( a_3 \)) is \( a_1 + 2d = 2 + 2 \times 3 = 8 \).
- The fourth term (\( a_4 \)) is \( a_1 + 3d = 2 + 3 \times 3 = 11 \).
So the sequence would be: \( 2, 5, 8, 11, \ldots \).
In general, the sequence can be written as:
\[ a_1, a_1 + d, a_1 + 2d, a_1 + 3d, \ldots \]
If you have specific values for \( a_1 \) and \( d \), you can generate the terms of the sequence accordingly!