Question

Choose the correct choice in the following and justify :
(i) ${30}^{th}$ term of the AP: $10,7,4,...$, is
(A) $97$ (B) $77$ (C) $-77$ (D) $87$
(ii) ${11}^{th}$ term of the AP: $-3,-\frac{1}{2},2$,...., is
(A) $28$ (B) $22$ (C) $38$ (D) $-48\frac{1}{2}$

Answer 1

(i) Given that
A.P. $10,7,4,\dots$
First term, $a=10$
Common difference, $d=a_2=a_1=7-10=-3$

We know that $a_n=a+(n-1)d$

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

$=10+\left(29\right)(-3)$

$=10-87$

$=-77$
Hence, the correct answer is option C.

(ii) A.P. is $-3,\frac{-1}{2},2,......$

First term $a=-3$
Common difference, $d=a_2-a_1=\frac{-1}{2}-(-3)=\frac{5}{2}$

We know that, $a_n=a+(n-1)d$

$a_{11}=-3+(11-1)\frac{5}{2}=-3+\left(10\right)\frac{5}{2}=-3+25=22$

Hence, the answer is option B.