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# 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

(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).