Question 2

Find the first five terms of the sequence in which the $n^{\text{th}}$ term is given by, for $n \ge 1$:

(i) $t_n = 3n - 4$

(ii) $t_n = 2 - 5n$

(iii) $t_n = n^2 - 2n + 3$

Determine whether 97 and 172 are terms of the sequence $t_n = 5n - 3$ for $n \ge 1$.

Which term of the sequence $t_n = 5n - 3$ for $n \ge 1$ is 607?

A sequence is given by the recursive rule $t_1 = -5$, $t_{n+1} = t_n + 3$ for $n \ge 1$. 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 $n \ge 4$. Find $T_4, T_5, T_6, T_7,$ and $T_8$.