Question

Write the next three rational numbers:

$\frac{1}{-6},\frac{2}{-12},\frac{3}{-18},\frac{4}{-24},.....,.....,.....$

Answer 1

Given pattern is,

$\frac{1}{-6},\frac{2}{-12},\frac{3}{-18},\frac{4}{-24},.....,.....,.....$

The first rational number is $\frac{1}{-6}$.

The second rational number is $\frac{1\times 2}{-6\times 2}=\frac{2}{-12}$.

The third rational number is $\frac{1\times 3}{-6\times 3}=\frac{3}{-18}$.

The fourth rational number is $\frac{1\times 4}{-6\times 4}=\frac{4}{-24}$.

So the next three rational numbers of this pattern are,

$\frac{1\times 5}{-6\times 5}=\frac{5}{-30}$, $\frac{1\times 6}{-6\times 6}=\frac{6}{-36}$ and $\frac{1\times 7}{-6\times 7}=\frac{7}{-42}$

Therefore the next three rational numbers are $\frac{5}{-30},\frac{6}{-36},\frac{7}{-42}$.