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  4. Find three arithmetic means between 3 and 19.

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

Sequences and Series

Solution:

Let $A_1, A_2, A_3$ be $3 A.M.’s$ 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 $7, 11, 15$.