Question

Insert six rational numbers between 3 and 4.

Answer 1

Let:
x = 3, y = 4 and n = 6
We know:
d = $\frac{y-x}{n+1}=\frac{4-3}{6+1}=\frac{1}{7}$
So, six rational numbers between x and y are:
(x + d), (x + 2d), (x + 3d), (x + 4d), (x + 5d) and (x + 6d)
= $\left(3+\frac{1}{7}\right),\left(3+\frac{2}{7}\right),\left(3+\frac{3}{7}\right),\left(3+\frac{4}{7}\right),\left(3+\frac{5}{7}\right)\mathrm{and}\left(3+\frac{6}{7}\right)$

= $\frac{22}{7},\frac{23}{7},\frac{24}{7},\frac{25}{7},\frac{26}{7}\mathrm{and}\frac{27}{7}$