Question

Find three arithmetic means between $3$ and $19$.

• A. $7,11,15$
• B. $5,10,15$
• C. $6,11,16$
• D. $5,7,9$

Answer 1

Answer: (A)

Let $A_1,A_2,A_3$ be $3A.M.’s$ between $3$ and $19$. Then $3,A_1,A_2,A_3,19$ are in $A.P$ . whose common difference is
$d=\frac{19-3}{4}=4$
$\therefore A_1=3+d$
$\Rightarrow A_1=7$,
$A_2=3+2d$
$\Rightarrow A_2=11$,
$A_3=3+3d$
$\Rightarrow A_3=15$,
Hence, the required $A.M.’s$ are $7,11,15$.