(i) 30th term of the AP: 10, 7, 4, . . . , is

(A) 97 (B) 77 (C) –77 (D) – 87

(ii) 11th term of the AP: – 3, -1/2, 2, . . ., is

(A) 28 (B) 22 (C) –38 (D) – 48 1/2

**Solution:**

**(i)** From the given,

A.P. = 10, 7, 4, …

Therefore, we can find,

First term, a = 10

Common difference, d = a_{2} − a_{1 }= 7 − 10 = −3

As we know, for an A.P.,

a_{n} = a + (n − 1) d

Putting the values;

a_{30} = 10 + (30 − 1)(−3)

a_{30} = 10 + (29)(−3)

a_{30} = 10 − 87 = −77

Hence, the correct answer is option C.

**(ii)** From the given,

A.P. = -3, -1/2, ,2 …

Therefore, we can find,

First term a = – 3

Common difference, d = a_{2} − a_{1} = (-1/2) – (-3)

⇒ (-1/2) + 3 = 5/2

As we know, for an A.P.,

a_{n} = a + (n − 1) d

Putting the values;

a_{11} = -3 + (11 – 1)(5/2)

a_{11} = -3 + (10)(5/2)

a_{11} = -3 + 25

a_{11} = 22

Hence, the correct answer is option B.