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Magazine Problem 1
Consider the sequence defined by the explicit formula \(A_{N}=N^{2}+1\) (a) Find \(A_{1}\). (b) Find \(A_{100}\). (c) Suppose \(A_{N}=10 .\) Find \(N\).
Problem 2
Consider the sequence defined by the explicit formula \(A_{N}=3^{N}-2\) (a) Find \(A_{3}\). (b) Use a calculator to find \(A_{15}\). (c) Suppose \(A_{N}=79 .\) Find \(N\).
Problem 3
Consider the sequence defined by the explicit formula \(A_{N}=\frac{4 N}{N+3}\) (a) Find \(A_{1}\). (b) Find \(A_{9}\). (c) Suppose \(A_{N}=\frac{5}{2},\) Find \(N\).
Problem 4
Consider the sequence defined by the explicit formula \(A_{N}=\frac{2 N+3}{3 N-1}\) (a) Find \(A_{1}\). (b) Find \(A_{100}\) - (c) Suppose \(A_{N}=1 .\) Find \(N\).
Problem 5
Consider the sequence defined by the explicit formula \(A_{N}=(-1)^{N+1}\) (a) Find \(A_{1}\) - (b) Find \(A_{100}\) - (c) Find all values of \(N\) for which \(A_{N}=1\).
Problem 6
Consider the sequence defined by the explicit formula \(A_{N}=\left(-\frac{1}{N}\right)^{N-1}\) (a) Find \(A_{1}\). (b) Find \(A_{4}\) (c) Find all values of \(N\) for which \(A_{N}\) is positive.
Problem 7
Consider the sequence defined by the recursive formula \(A_{N}=2 A_{N-1}+A_{N-2}\) and starting with \(A_{1}=1, A_{2}=1\) (a) List the next four terms of the sequence. (b) Find \(A_{8}\).
Problem 8
Consider the sequence defined by the recursive formula \(A_{N}=A_{N-1}+2 A_{N-2}\) and starting with \(A_{1}=1, A_{2}=1\) (a) List the next four terms of the sequence. (b) Find \(A_{8}\).
Problem 9
Consider the sequence defined by the recursive formula \(A_{N}=A_{N-1}-2 A_{N-2}\) and starting with \(A_{1}=1, A_{2}=-1\) (a) List the next four terms of the sequence. (b) Find \(A_{8}\).
Problem 10
Consider the sequence defined by the recursive formula \(A_{N}=2 A_{N-1}-3 A_{N-2}\) and starting with \(A_{1}=-1, A_{2}=1\) (a) List the next four terms of the sequence. (b) Find \(A_{8}\).
