This question is from NCERT Book class 10th Ch. no.5 Ex. 5.2 Q. 1 . In this question you have to find the right option and support your answer by giving its solution. Answer the question with brief explanation.

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

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(i) Given here,

A.P. = 10, 7, 4, …

Therefore, we can find,

First term,

a= 10Common difference,

d=a_{2}−a_{1 }= 7−10 = −3As we know, for an A.P.,

a=_{n}a+(n−1)dPutting the values;

a_{30}= 10+(30−1)(−3)a_{30}= 10+(29)(−3)a_{30}= 10−87 = −77Hence, the correct answer is option C.

(ii) Given here,

A.P. = -3, -1/2, ,2 …

Therefore, we can find,

First term

a= – 3Common 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)dPutting the values;

a_{11}= 3+(11-1)(5/2)a_{11}= 3+(10)(5/2)a_{11}= -3+25a_{11}= 22Hence, the answer is option B.