Question

you are sitting in row 23 and notice there are 65 seats in your row. the row in front of you has 63 seats and the row behind you has 67 seats. what is the common difference? 2 65 42 23

Explanation:

Step1: Identify the arithmetic sequence terms

Let the number of seats in the row in front of you (row 22) be \( a_{n - 1}=63 \), your row (row 23) be \( a_{n}=65 \), and the row behind you (row 24) be \( a_{n + 1}=67 \).

Step2: Use the arithmetic sequence common difference formula

The common difference \( d \) in an arithmetic sequence is given by \( d=a_{n}-a_{n - 1} \) (or \( d=a_{n + 1}-a_{n} \)). Using \( a_{n}=65 \) and \( a_{n - 1}=63 \), we calculate \( d = 65-63=2 \). We can also verify with \( a_{n + 1}-a_{n}=67 - 65 = 2 \).

Answer:

2