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) $-48$

To do:

We have to choose the correct choice in each case.

Solution:

(i) Given AP is $10, 7, 4, …$

$a=10, d=7-10=-3, n=30$

We know that,

$a_{n}=a+(n-1) d$

$a_{30}=10+(30-1)(-3)$

$=10+29(-3)$

$=10-87$

Hence, C is the correct choice.

(ii) Given AP is $-3, -\frac{1}{2},, 2, …,$

$a=-3$

$d=-\frac{1}{2}-(-3)=-\frac{1}{2}+3$

$=\frac{-1+6}{2}$

$=\frac{5}{2}$

$n=11$

We know that,

$a_{n}=a+(n-1) d$

$a_{11}=-3+(11-1)(\frac{5}{2})$

$=-3+10(\frac{5}{2})$

$=-3+5(5)$

 $=-3+25$

$=22$

Hence, B is the correct choice. 

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Updated on: 10-Oct-2022

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