1. Problem 3 (1979): Find the value of \(\alpha\) so that the sequence \(a_n = \alpha n + 5\) satisfies a given condition.\n\nSince no other condition is stated, we assume the problem wants the general form with \(\alpha\) as a parameter.\n\n2. Problem 4 (1969): Determine the next number in the sequence 2, 8, 14, 20, ...\n\nStep 1: Identify the pattern in the sequence: 2, 8, 14, 20, ...\nStep 2: Calculate the differences between consecutive terms: \(8 - 2 = 6\), \(14 - 8 = 6\), \(20 - 14 = 6\)\nStep 3: Since the difference is constant at 6, this is an arithmetic sequence with common difference \(d=6\).\nStep 4: The next term \(a_5 = a_4 + d = 20 + 6 = 26\n\nFinal answers:\n3. \(\alpha\) is a free parameter in \(a_n = \alpha n + 5\), the sequence depends on \(\alpha\)\n4. The next number in the sequence is \(26\).