Question 1

We will substitute the values of $n$ from 1 to 5 into each given formula.

Step 1 — Find terms for $t_n = 3n - 4$

Let's find the first term by setting $n = 1$.

$t_1 = 3(1) - 4$

$= 3 - 4$

$\boxed{-1}$

Let's find the second term by setting $n = 2$.

$t_2 = 3(2) - 4$

$= 6 - 4$

$\boxed{2}$

Let's find the third term by setting $n = 3$.

$t_3 = 3(3) - 4$

$= 9 - 4$

$\boxed{5}$

Let's find the fourth term by setting $n = 4$.

$t_4 = 3(4) - 4$

$= 12 - 4$

$\boxed{8}$

Let's find the fifth term by setting $n = 5$.

$t_5 = 3(5) - 4$

$= 15 - 4$

$\boxed{11}$

Step 2 — Find terms for $t_n = 2 - 5n$

Let's find the first term by setting $n = 1$.

$t_1 = 2 - 5(1)$

$= 2 - 5$

$\boxed{-3}$

Let's find the second term by setting $n = 2$.

$t_2 = 2 - 5(2)$

$= 2 - 10$

$\boxed{-8}$

Let's find the third term by setting $n = 3$.

$t_3 = 2 - 5(3)$

$= 2 - 15$

$\boxed{-13}$

Let's find the fourth term by setting $n = 4$.

$t_4 = 2 - 5(4)$

$= 2 - 20$

$\boxed{-18}$

Let's find the fifth term by setting $n = 5$.

$t_5 = 2 - 5(5)$

$= 2 - 25$

$\boxed{-23}$

Step 3 — Find terms for $t_n = n^2 - 2n + 3$

Let's find the first term by setting $n = 1$.

$t_1 = 1^2 - 2(1) + 3$

$= 1 - 2 + 3$

$\boxed{2}$

Let's find the second term by setting $n = 2$.

$t_2 = 2^2 - 2(2) + 3$

$= 4 - 4 + 3$

$\boxed{3}$

Let's find the third term by setting $n = 3$.

$t_3 = 3^2 - 2(3) + 3$

$= 9 - 6 + 3$

$\boxed{6}$

Let's find the fourth term by setting $n = 4$.

$t_4 = 4^2 - 2(4) + 3$

$= 16 - 8 + 3$

$\boxed{11}$

Let's find the fifth term by setting $n = 5$.

$t_5 = 5^2 - 2(5) + 3$

$= 25 - 10 + 3$

$\boxed{18}$

Answer

(i) The first five terms are -1, 2, 5, 8, 11. (ii) The first five terms are -3, -8, -13, -18, -23. (iii) The first five terms are 2, 3, 6, 11, 18.