Exercise 8.1

Find the first five terms of the sequence in which the \(n^{th}\) term is given by \(t_n = 3n − 4\) for \(n ≥ 1\).

Find the first five terms of the sequence in which the \(n^{th}\) term is given by \(t_n = 2 − 5n\) for \(n ≥ 1\).

Find the first five terms of the sequence in which the \(n^{th}\) term is given by \(t_n = n^2 − 2n + 3\) for \(n ≥ 1\).

Find the \(10^{th}\) and \(15^{th}\) terms of the sequence \(t_n = 5n − 3\) for \(n ≥ 1\).

Determine whether 97 and 172 are terms of the sequence \(t_n = 5n − 3\) for \(n ≥ 1\).

Which term of the sequence \(t_n = 5n − 3\) for \(n ≥ 1\) is 607?

A sequence is given by the recursive rule \(t_1 = −5, t_{n+1} = t_n + 3\) for \(n ≥ 1\). Find the first five terms of the sequence. Is 52 a term of this sequence? If so, which term is it?

Let \(T_1 = 1, T_2 = 2, T_3 = 4, \,and\, T_n = T_{n−1} + T_{n−2} + T_{n−3}\) for n ≥ 4. Find \(T_4, T_5, T_6, T_7,\,and\, T_8\).