Julia owns 13 books. She buys two new books every week. Which arithmetic sequence describes the number of books she has? A. \( a_{1}=13 ; a_{n}=a_{n+1}+2 \) B. \( a_{1}=2 ; a_{n}=a_{n+1}+13 \) C. \( a_{1}=2 ; a_{n}=a_{n-1}+13 \) D. \( a_{1}=13 ; a_{n}=a_{n-1}+2 \)

To determine the correct arithmetic sequence that describes the number of books Julia has, let's break down the information: 1. **Initial Number of Books**: Julia starts with 13 books. This means the first term of the sequence, \( a_1 \), is 13. 2. **Weekly Addition**: Julia buys 2 new books every week. In an arithmetic sequence, the common difference (\( d \)) is the constant amount added each term. Here, \( d = 2 \). 3. **General Formula**: The \( n \)-th term of an arithmetic sequence can be described by the formula: \[ a_n = a_{n-1} + d \] Substituting the known values: \[ a_n = a_{n-1} + 2 \] Putting it all together, the correct arithmetic sequence is: \[ a_1 = 13; \quad a_n = a_{n-1} + 2 \] **Answer:** **D.** \( a_{1}=13 ; a_{n}=a_{n-1}+2 \)