Question 2

We find each term by adding the common difference to the previous term.

Step 1 — Calculate terms for (i)

Here, the first term $a$ is 10. The common difference $d$ is 10. Let's find the first term $a_1$. $a_1 = a$ $a_1 = 10$ Let's find the second term $a_2$. $a_2 = a_1 + d$ $a_2 = 10 + 10$ $= 20$ Let's find the third term $a_3$. $a_3 = a_2 + d$ $a_3 = 20 + 10$ $= 30$ Let's find the fourth term $a_4$. $a_4 = a_3 + d$ $a_4 = 30 + 10$ $= 40$ The first four terms are:

$\boxed{10, 20, 30, 40}$

Step 2 — Calculate terms for (ii)

Here, the first term $a$ is -2. The common difference $d$ is 0. Let's find the first term $a_1$. $a_1 = a$ $a_1 = -2$ Let's find the second term $a_2$. $a_2 = a_1 + d$ $a_2 = -2 + 0$ $= -2$ Let's find the third term $a_3$. $a_3 = a_2 + d$ $a_3 = -2 + 0$ $= -2$ Let's find the fourth term $a_4$. $a_4 = a_3 + d$ $a_4 = -2 + 0$ $= -2$ The first four terms are:

$\boxed{-2, -2, -2, -2}$

Step 3 — Calculate terms for (iii)

Here, the first term $a$ is 4. The common difference $d$ is -3. Let's find the first term $a_1$. $a_1 = a$ $a_1 = 4$ Let's find the second term $a_2$. $a_2 = a_1 + d$ $a_2 = 4 + (-3)$ $= 1$ Let's find the third term $a_3$. $a_3 = a_2 + d$ $a_3 = 1 + (-3)$ $= -2$ Let's find the fourth term $a_4$. $a_4 = a_3 + d$ $a_4 = -2 + (-3)$ $= -5$ The first four terms are:

$\boxed{4, 1, -2, -5}$

Step 4 — Calculate terms for (iv)

Here, the first term $a$ is -1. The common difference $d$ is $\frac{1}{2}$. Let's find the first term $a_1$. $a_1 = a$ $a_1 = -1$ Let's find the second term $a_2$. $a_2 = a_1 + d$ $a_2 = -1 + \frac{1}{2}$ $= -\frac{1}{2}$ Let's find the third term $a_3$. $a_3 = a_2 + d$ $a_3 = -\frac{1}{2} + \frac{1}{2}$ $= 0$ Let's find the fourth term $a_4$. $a_4 = a_3 + d$ $a_4 = 0 + \frac{1}{2}$ $= \frac{1}{2}$ The first four terms are:

$\boxed{-1, -\frac{1}{2}, 0, \frac{1}{2}}$

Step 5 — Calculate terms for (v)

Here, the first term $a$ is -1.25. The common difference $d$ is -0.25. Let's find the first term $a_1$. $a_1 = a$ $a_1 = -1.25$ Let's find the second term $a_2$. $a_2 = a_1 + d$ $a_2 = -1.25 + (-0.25)$ $= -1.50$ Let's find the third term $a_3$. $a_3 = a_2 + d$ $a_3 = -1.50 + (-0.25)$ $= -1.75$ Let's find the fourth term $a_4$. $a_4 = a_3 + d$ $a_4 = -1.75 + (-0.25)$ $= -2.00$ The first four terms are:

$\boxed{-1.25, -1.50, -1.75, -2.00}$

Answer

(i) The first four terms are $10, 20, 30, 40$. (ii) The first four terms are $-2, -2, -2, -2$. (iii) The first four terms are $4, 1, -2, -5$. (iv) The first four terms are $-1, -\frac{1}{2}, 0, \frac{1}{2}$. (v) The first four terms are $-1.25, -1.50, -1.75, -2.00$.