Question

Write the next three rational numbers:

$\frac{-8}{7},\frac{-16}{14},\frac{-24}{21},\frac{-32}{28},.....,.....,.....$

Answer 1

Given pattern is,

$\frac{-8}{7},\frac{-16}{14},\frac{-24}{21},\frac{-32}{28},.....,.....,.....$

The first rational number is$\frac{-8}{7}$.

The second rational number is$\frac{-8\times 2}{7\times 2}=\frac{-16}{14}$.

The third rational number is$\frac{-8\times 3}{7\times 3}=\frac{-24}{21}$.

The fourth rational number is$\frac{-8\times 4}{7\times 4}=\frac{-32}{28}$.

So the next three rational numbers of this pattern are,

$\frac{-8\times 5}{7\times 5}=\frac{-40}{35}$, $\frac{-8\times 6}{7\times 6}=\frac{-48}{42}$ and $\frac{-8\times 7}{7\times 7}=\frac{-56}{49}$

Therefore the next three rational numbers are$\frac{-40}{35},\frac{-48}{42},\frac{-56}{49}$.