The sequence \(a_1, a_2, a_3, \dots, a_n\) is defined by \(a_n = 9 + a_{n-1}\) for each integer \(n \ge 2\). If \(a_1 = 11\), what is the value of \(a_{34}\)?
Explanation: The sequence is an arithmetic progression with a common difference of \(d=9\). The formula for the \(n\)-th term is \(a_n = a_1 + (n-1)d\). We need to find \(a_{34}\). \(n=34\), \(a_1=11\), \(d=9\). \(a_{34} = a_1 + (34-1)d = 11 + (33) \times 9\). \(33 \times 9 = 297\). \(a_{34} = 11 + 297 = 308\).
