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)

$7, 11, 15$

Answer 2

Let $A_1, A_2, A_3$ be $3 A.M.??$ 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 $A.M.??$ are $7, 11, 15$.