Find six rational numbers between 2 and 3.

Question:

Find six rational numbers between 2 and 3.

Solution:

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

$(x+d),(x+2 d),(x+3 d), \ldots,(x+n d)$

$=\left(2+\frac{1}{7}\right),\left(2+2 \times \frac{1}{7}\right),\left(2+3 \times \frac{1}{7}\right),\left(2+4 \times \frac{1}{7}\right),\left(2+5 \times \frac{1}{7}\right),\left(2+6 \times \frac{1}{7}\right)$

$=\frac{15}{7}, \frac{16}{7}, \frac{17}{7}, \frac{18}{7}, \frac{19}{7}, \frac{20}{7}$