Answer :
Answer:
Step-by-step explanation:
To determine the first 4 numbers in the sequence and the constant difference in an arithmetic sequence, you need to start by understanding the pattern. Let's break this down:
### Arithmetic Sequence Basics:
An arithmetic sequence is characterized by a constant difference between consecutive terms. The general form of an arithmetic sequence is:
\[ a_n = a_1 + (n-1)d \]
where:
- \( a_n \) is the \( n \)-th term,
- \( a_1 \) is the first term,
- \( d \) is the common difference,
- \( n \) is the position of the term in the sequence.
### Given Problem:
The problem refers to the number sequence associated with street lights positioned at house numbers. To solve this, you need to:
1. Identify the initial term (\( a_1 \)).
2. Find the common difference (\( d \)).
#### Example Calculation:
Let's assume we need to find the first 4 terms and the common difference of a sequence given the positions of street lights:
1. **Identify the first term (\( a_1 \)) and the common difference (\( d \))**:
Suppose the house numbers (positions of the street lights) are given or identified as:
- House 1: \( a_1 \)
- House 2: \( a_1 + d \)
- House 3: \( a_1 + 2d \)
- House 4: \( a_1 + 3d \)
If you were given specific house numbers where street lights are positioned, you could use these numbers to determine \( a_1 \) and \( d \).
2. **Example**:
Let’s say the house numbers are given as follows:
- House 1: 3
- House 2: 7
- House 3: 11
- House 4: 15
To determine the constant difference (\( d \)):
- Difference between House 2 and House 1: \( 7 - 3 = 4 \)
- Difference between House 3 and House 2: \( 11 - 7 = 4 \)
- Difference between House 4 and House 3: \( 15 - 11 = 4 \)
The constant difference \( d \) is 4.
3. **Sequence Determination**:
The sequence is \( 3, 7, 11, 15 \), with each number showing the position of the street light at each house number.
### Conclusion:
For the arithmetic sequence based on street light positions:
- **First 4 terms**: 3, 7, 11, 15
- **Constant difference**: 4
