\( \begin{array}{l}13 \text { Find the } n \text {th term of each sequence. } \\ \begin{array}{l}\text { (a) } \\ 21,\end{array} \quad 13, \quad 5, \quad-3, \quad-11, \\ \text { (b) } \\ 2.5, \\ 5,\end{array} 10, \quad 20, \quad 40, \quad \ldots \)

The first sequence, where the numbers are \(21, 13, 5, -3, -11\), is an arithmetic sequence with a common difference of \(-8\). To find the \(n\)th term, we use the formula \(a_n = a_1 + (n-1)d\), where \(a_1 = 21\) and \(d = -8\). Thus, the \(n\)th term is given by \(a_n = 21 + (n-1)(-8) = 29 - 8n\). In the second sequence, \(2.5, 5, 10, 20, 40, \ldots\), it’s a geometric sequence with a common ratio of \(2\). The \(n\)th term can be determined using the formula \(a_n = a_1 \cdot r^{n-1}\), where \(a_1 = 2.5\) and \(r = 2\). Therefore, the \(n\)th term is \(a_n = 2.5 \cdot 2^{n-1}\).