Question

If $A_1,A_2$are two AMs between $1/3$ and $1/24$, then their values are

• A. $7/72,5/36$
• B. $17/72,5/36$
• C. $7/36,5/72$
• D. $5/72,17/72$

Answer 1

The correct option is B

$17/72,5/36$

Step 1. Express the given data :

Given $A_1$and $A_2$are $2$AM’s between $1/3$ and $1/24$.

So $1/3,A_1,A_2,1/24$are in AP.

Here$a=1/3,a_4=1/24$.

Step2. Find the value of $d$:

$$\begin{gathered} a_4=a+3d=1/24\left[\because a_n=a+(n-1)d\right] \\ \Rightarrow \frac{1}{3}+3d=\frac{1}{24} \\ \Rightarrow 3d=\frac{1}{24}–\frac{1}{3} \\ \Rightarrow 3d=\frac{-7}{24} \\ \Rightarrow d=-7/72 \end{gathered}$$

Step 3. Find the value of $A_1$and $A_2$:

The second term is

$$\begin{gathered} A_1=a+(2-1)d \\ \Rightarrow A_1=a+d \\ \Rightarrow A_1=\frac{1}{3}-\frac{7}{72} \\ \Rightarrow A_1=\frac{17}{72} \end{gathered}$$

The Third term is

, $$\begin{gathered} A_2=A_1+d \\ \Rightarrow A_2=\frac{17}{72}-\frac{7}{72} \\ \Rightarrow A_2=\frac{10}{72} \\ \Rightarrow A_2=\frac{5}{36} \end{gathered}$$

Hence, the correct option is (B).