Question

The four arithmetic means between $3$ and $23$ are

• A. $5,9,11,13$
• B. $7,11,15,19$
• C. $5,11,15,22$
• D. $7,15,19,21$

Answer 1

The correct option is B

$7,11,15,19$

Find the arithmetic mean between given numbers

We need to find four arithmetic means between $3$ and $23$

Let $a+d,a+2d,a+3d$ and $a+4d$ be the four arithmetic means between $3$ and $23$.

Here, $a=3$

$$\begin{gathered} \Rightarrow a+5d=23 \\ \Rightarrow 3+5d=20 \\ \Rightarrow 5d=20 \\ \Rightarrow d=4 \\ \Rightarrow a+d=7 \\ \Rightarrow a+2d=11 \\ \Rightarrow a+3d=15 \\ \Rightarrow a+4d=19 \end{gathered}$$

So the four arithmetic means are $7,11,15,19$.

Hence , the four arithmetic means between $3$ and $23$ are $7,11,15,19$.