Insert four arithmetic means between 4 and 29

Solution:

To find: Four arithmetic means between 4 and 29

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 4 and 29

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

$d=\frac{29-4}{4+1}$

$d=\frac{25}{5}$

$d=5$

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

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

= 4 + 5

= 9

Second arithmetic mean, $A_{2}=a+2 d$

$=4+2(5)$

$=4+10$

$=14$

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

$=4+3(5)$

$=4+15$

= 19

Fourth arithmetic mean, $\mathrm{A}_{4}=\mathrm{a}+4 \mathrm{~d}$

$=4+4(5)$

$=4+20$

$=24$

Ans) The four arithmetic means between 4 and 29 are 9, 14, 19 and 24