A bus takes (7) passengers at the first stop and (2) more passengers board at each next stop. How many passengers board at the (10)th stop?

Correct answer: 25

The numbers of passengers boarding form an arithmetic progression: 7, 9, 11, \(\ldots\). Here, the first term is \(a=7\), the common difference is \(d=2\), and \(n=10\). Thus, \(a_{10}=a+(n-1)d=7+(10-1)\times2=25\). Therefore, 25 passengers board at the 10th stop. Getting 23 usually results from using the term number incorrectly. Exam tip: for the \(n\)th term of an AP, use \(a_n=a+(n-1)d\).