Question

Find six rational numbers between 2 and 3.

Answer 1

x = 2, y = 3 and n = 6
$d=\frac{y-x}{n+1}=\frac{3-2}{6+1}=\frac{1}{7}$
Thus, the required numbers are
$$\begin{gathered} \left(x+d\right),\left(x+2d\right),\left(x+3d\right),...,\left(x+nd\right) \\ =\left(2+\frac{1}{7}\right),\left(2+2\times \frac{1}{7}\right),\left(2+3\times \frac{1}{7}\right),\left(2+4\times \frac{1}{7}\right),\left(2+5\times \frac{1}{7}\right),\left(2+6\times \frac{1}{7}\right) \\ =\frac{15}{7},\frac{16}{7},\frac{17}{7},\frac{18}{7},\frac{19}{7},\frac{20}{7} \end{gathered}$$