Question 1

What is the 10th term of the arithmetic progression: 2, 7, 12, ...?

Accepted Answer

To find the 10th term ($a{10}$) of the arithmetic progression (AP), we use the formula $an = a + (n - 1)d$. Here, the first term $a = 2$, and the common difference $d = 7 - 2 = 5$. Substituting $n = 10$, we get $a{10} = 2 + (10 - 1)5 = 2 + (9)5 = 2 + 45 = 47$. Therefore, the correct option is C.

Question 2

What is the common difference of the AP: -5, -1, 3, 7, ...?

Accepted Answer

The common difference ($d$) of an AP is found by subtracting any term from its succeeding term, $d = a{2} - a{1}$. Here, $a1 = -5$ and $a2 = -1$. Therefore, $d = (-1) - (-5) = -1 + 5 = 4$. Thus, the correct option is B.

Question 3

Which term of the AP: 3, 8, 13, 18, ... is 78?

Accepted Answer

Given the AP: $a = 3$, $d = 8 - 3 = 5$, and $an = 78$. Using the formula $an = a + (n - 1)d$, we get $78 = 3 + (n - 1)5 \implies 75 = (n - 1)5 \implies n - 1 = 15 \implies n = 16$. Therefore, the 16th term is 78, making option C correct.

Question 4

What is the 30th term of the AP: 10, 7, 4, ...?

Accepted Answer

Here, $a = 10$, $d = 7 - 10 = -3$, and $n = 30$. Using $an = a + (n - 1)d$, we find $a{30} = 10 + (30 - 1)(-3) = 10 + 29(-3) = 10 - 87 = -77$. Thus, the correct option is C.

Question 5

Find the 11th term of the AP: -3, -1/2, 2, ...

Accepted Answer

Here, $a = -3$, $d = -1/2 - (-3) = -1/2 + 3 = 5/2$, and $n = 11$. Using $a{11} = a + (11 - 1)d = -3 + 10(5/2) = -3 + 25 = 22$. Therefore, the correct option is B.

Arithmetic Progressions