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An arithmetic sequence is such that \(u_1 = \log_c (p)\) and \(u_2 = \log_c (pq)\) where \(c > 1\), and \(p, q > 0\).

1. Show that \(d = \log_c (q)\).
2. Let \(p = c^2\) and \(q = c^3\). Find the value of \(\sum_{n=1}^{20} u_n\).