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Question

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: 3,12,2,...., is
(A) 28 (B) 22 (C) 38 (D) 4812

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Solution

(i) Given that
A.P. 10,7,4,
First term, a=10
Common difference, d=a2=a1=710=3
We know that an=a+(n1)d
a30=10+(301)(3)
=10+(29)(3)
=1087
=77
Hence, the correct answer is option C.

(ii) A.P. is 3,12,2,......
First term a=3
Common difference, d=a2a1=12(3)=52
We know that, an=a+(n1)d
a11=3+(111)52=3+(10)52=3+25=22
Hence, the answer is option B.

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