Insert three arithmetic means between 23 and 7.

Solution:

To find: Three arithmetic means between 23 and 7

Formula used: (i) $d=\frac{b-a}{n+1}$, where, $d$ is the common difference

n is the number of arithmetic means

(ii) $A_{n}=a+n d$

We have 23 and 7

Using Formula, $d=\frac{b-a}{n+1}$

$d=\frac{7-23}{3+1}$

$d=\frac{-16}{4}$

$d=-4$

Using Formula, $A_{n}=a+n d$

First arithmetic mean, $A_{1}=a+d$

$=23+(-4)$

$=19$

Second arithmetic mean, $\mathrm{A}_{2}=\mathrm{a}+2 \mathrm{~d}$

$=23+2(-4)$

$=23+(-8)$

$=15$

Third arithmetic mean, $\mathrm{A}_{3}=\mathrm{a}+3 \mathrm{~d}$

$=23+3(-4)$

$=23+(-12)$

$=11$

Ans) The three arithmetic means between 23 and 7 are 19,15 and 11