Choose the correct choice in the following and justify:
(i) 30th term of the AP : \(10, 7, 4…....\) is
(A) 97
(B) 77
(C) –77
(D) –87

(ii) 11th term of the AP : \(-3, \frac{1}{2}, 2…...\) is
(A) 28
(B) 22
(C) –38
(D) \({-48}{\dfrac{1}{2}}\)

(i) 10, 7, 4…
First term = a = 10,
Common difference = d
= 7 – 10 = 4 – 7 = –3
And n = 30{Because, we need to find 30th term}

\(a_n = a + (n - 1)d\)
= \(a_{30}\)
= 10 + (30 - 1) (-3)
= 10 – 87 = -77

Therefore, the answer is (C).


(ii) -3, \({{-1} \over {2}}\) , 2…
First term = a = –3,
Common difference = d
= \({{-1} \over {2}} - (-3) = 2 - ({{-1} \over {2}}) = {{5} \over {2}}\)
And n = 11 (Because, we need to find 11th term)

= -3 + (11 – 1) \({{5} \over {2}}\)
= -3 + 25 = 22

Therefore 11th term is 22 which means answer is (B).