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Magazine Problem 1
Find the first six terms of each of the following sequences, starting with \(n=1\). \(a_{n}=1+(-1)^{n}\) for \(n \geq 1\)
Problem 2
Find the first six terms of each of the following sequences, starting with \(n=1\). \(a_{n}=n^{2}-1\) for \(n \geq 1\)
Problem 3
Find the first six terms of each of the following sequences, starting with \(n=1\). \(a_{1}=1\) and \(a_{n}=a_{n-1}+n\) for \(n \geq 2\)
Problem 4
Find the first six terms of each of the following sequences, starting with \(n=1\). \(\quad a_{1}=1, \quad a_{2}=1\) and \(a_{n+2}=a_{n}+a_{n+1}\) for \(n \geq 1\)
Problem 5
Find an explicit formula for \(a_{n}\) where \(a_{1}=1\) and \(a_{n}=a_{n-1}+n\) for \(n \geq 2\).
Problem 6
Find a formula \(a_{n}\) for the \(n\) th term of the arithmetic sequence whose first term is \(a_{1}=1\) such that \(a_{n-1}-a_{n}=17\) for \(n \geq 1\).
Problem 7
Find a formula \(a_{n}\) for the \(n\) th term of the arithmetic sequence whose first term is \(a_{1}=-3\) such that \(a_{n-1}-a_{n}=4\) for \(n \geq 1\).
Problem 8
Find a formula \(a_{n}\) for the \(n\) th term of the geometric sequence whose first term is \(a_{1}=1\) such that \(\frac{a_{n+1}}{a_{n}}=10\) for \(n \geq 1\).
Problem 9
Find a formula \(a_{n}\) for the \(n\) th term of the geometric sequence whose first term is \(a_{1}=3\) such that \(\frac{a_{n+1}}{a_{n}}=1 / 10\) for \(n \geq 1\).
Problem 10
Find an explicit formula for the \(n\) th term of the sequence whose first several terms are \(\\{0,3,8,15,24,35,48,63,80,99, \ldots\\} .\)
