Sequences And Series Ques 14
- Which of the following statements is correct?
(a) $A_1>A_2>A_3>\ldots$
(b) $A_1<A_2<A_1<\ldots$
(c) $A_1>A_3>A_5>\ldots$ and $A_2<A_4<A_6<\ldots$
(d) $A_1<A_3<A_5<\ldots$ and $A_2>A_4>A_6>\ldots$
Show Answer
Answer:
Correct Answer: 14.(a)
Solution: (a) $A_2$ is $AM$ of $A_1$ and $H_1$ and $A_1>H_1$
$\Rightarrow \quad A_1>A_2>H_1$
$A_3$ is $\mathrm{AM}$ of $A_2$ and $H_2$ and $A_2>H_2$
$\Rightarrow \quad$ $ A_2>A_3>H_2 $
$\therefore \quad A_1>A_2>A_2>\ldots$
BETA
