Question 1

We will use the formula for the $n^{\text{th}}$ term of an arithmetic progression.

Step 1 — Find the first term and common difference

First, let's identify the first term. The first term of the AP is 3. Let's find the common difference. We subtract any term from its next term.

$d = 8 - 3$

$\boxed{d = 5}$

Step 2 — Calculate the 10th term

The formula for the $n^{\text{th}}$ term is $t_n = a + (n-1)d$. Here, $a = \mathbf{3}$ and $d = \mathbf{5}$. We need to find the $10^{\text{th}}$ term, so $n = \mathbf{10}$. Let's substitute these values into the formula.

$t_{10} = 3 + (10 - 1) \times 5$

$= 3 + (9) \times 5$

$= 3 + 45$

$\boxed{t_{10} = 48}$

Step 3 — Calculate the 26th term

We use the same formula. Again, $a = \mathbf{3}$ and $d = \mathbf{5}$. Now we need the $26^{\text{th}}$ term, so $n = \mathbf{26}$. Let's put these values into the formula.

$t_{26} = 3 + (26 - 1) \times 5$

$= 3 + (25) \times 5$

$= 3 + 125$

$\boxed{t_{26} = 128}$

Answer

(i) The $10^{\text{th}}$ term is 48. (ii) The $26^{\text{th}}$ term is 128.