Consider an arithmetic sequence with \(u_1 = 0.6\) and \(u_4 = 0.15\).
Find the common difference, \(d\).
[2]The following The following table shows the probability distribution of a discrete random variable \(X\) such that \(\mathrm{P}(X = n) = \frac{u_n}{k}\), where \(n \in \mathbb{Z}^+\), \(1 \leq n \leq 4\) and \(k \in \mathbb{R}^+\).
| \(n\) | \(1\) | \(2\) | \(3\) | \(4\) |
|---|---|---|---|---|
| \(\mathrm{P}(X = n)\) | \(\frac{0.6}{k}\) | \(\frac{u_2}{k}\) | \(\frac{u_3}{k}\) | \(\frac{0.15}{k}\) |
Find the value of \(k\).
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