Question
What is the initial value and rate of change on a graph of an arithmetic sequence with d=2 and a1=4 ?
Answers
GPT-4o mini
In an arithmetic sequence, the initial value (the first term) is denoted as \( a_1 \). In this case, you provided \( a_1 = 4 \).
The rate of change in an arithmetic sequence is represented by the common difference \( d \). You mentioned that \( d = 2 \).
Thus, for the arithmetic sequence defined by the values you provided:
- The initial value is \( a_1 = 4 \).
- The rate of change is \( d = 2 \).
This means that each subsequent term in the sequence will increase by 2 from the previous term. The sequence can be represented as follows:
- First term: \( 4 \)
- Second term: \( 4 + 2 = 6 \)
- Third term: \( 6 + 2 = 8 \)
- Fourth term: \( 8 + 2 = 10 \)
- And so on.
In summary:
- Initial value: \( 4 \)
- Rate of change: \( 2 \)
The rate of change in an arithmetic sequence is represented by the common difference \( d \). You mentioned that \( d = 2 \).
Thus, for the arithmetic sequence defined by the values you provided:
- The initial value is \( a_1 = 4 \).
- The rate of change is \( d = 2 \).
This means that each subsequent term in the sequence will increase by 2 from the previous term. The sequence can be represented as follows:
- First term: \( 4 \)
- Second term: \( 4 + 2 = 6 \)
- Third term: \( 6 + 2 = 8 \)
- Fourth term: \( 8 + 2 = 10 \)
- And so on.
In summary:
- Initial value: \( 4 \)
- Rate of change: \( 2 \)