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

(A) $t_n = 3n - 4$, (B) $t_n = 2 - 5n$, and (C) $t_n = n^2 - 2n + 3$, for $n \geq 1$.                       [Page No. 179]

(A) $t_n = 3n - 4$:

$$t_1 = 3(1) - 4 = -1$$

$$t_2 = 3(2) - 4 = 2$$

$$t_3 = 3(3) - 4 = 5$$

$$t_4 = 3(4) - 4 = 8$$

$$t_5 = 3(5) - 4 = 11$$

First five terms: -1, 2, 5, 8, 11

(B) $t_n = 2 - 5n$

$$t_1 = 2 - 5 = -3$$

$$t_2 = 2 - 10 = -8$$

$$t_3 = 2 - 15 = -13$$

$$t_4 = 2 - 20 = -18$$

$$t_5 = 2 - 25 = -23$$

First five terms: -3, -8, -13, -18, -23

(C) $t_n = n^2 - 2n + 3$:

$$t_1 = 1 - 2 + 3 = 2$$

$$t_2 = 4 - 4 + 3 = 3$$

$$t_3 = 9 - 6 + 3 = 6$$

$$t_4 = 16 - 8 + 3 = 11$$

$$t_5 = 25 - 10 + 3 = 18$$

First five terms: 2, 3, 6, 11, 18