Question

Given the Recursive Formula:

a1 = 5

a4 = an−1 +2

(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
What is the common difference? Response area
What is the first term? Response area

Which term of the sequence does a4
represent? Response area

Which term does an−1
represent?

Answer 1

Let's analyze the recursive formula provided:

1. **First term:** The first term \( a_1 \) is given as \( 5 \).
- **Response for first term:** 5

2. **Common difference:** The formula indicates \( a_n = a_{n-1} + 2 \) for \( n \geq 2 \). This implies that each term after the first term increases by \( 2 \).
- **Response for common difference:** 2

3. **Which term does \( a_4 \) represent?** Since \( a_4 \) is the 4th term of the sequence, it directly represents the 4th term.
- **Response for which term \( a_4 \) represents:** 4

4. **Which term does \( a_{n-1} \) represent?** In the recursive definition, \( a_{n-1} \) refers to the term before \( a_n \). Thus it represents the \( (n-1)^{th} \) term of the sequence.
- **Response for which term \( a_{n-1} \) represents:** n-1

In summary:
- What is the common difference? **2**
- What is the first term? **5**
- Which term of the sequence does \( a_4 \) represent? **4**
- Which term does \( a_{n-1} \) represent? **n-1**