Sequences And Series Ques 14

  1. Which of the following statements is correct?

(a) $A_1>A_2>A_3>\ldots$

(b) $A_1<A_2<A_3<\ldots$

(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 $

$\therefore \quad A_1>A_2>A_3>\ldots$

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