Question

Write four more rational numbers in each of the following patterns:
(i) $\frac{-3}{5},\frac{-6}{10},\frac{-9}{15},\frac{-12}{20},...$

(ii) $\frac{-1}{4},\frac{-2}{8},\frac{-3}{12},...$

Answer 1

i) $\frac{-3}{5},\frac{-6}{10},\frac{-9}{15},\frac{-12}{20},...$

It can be observed that numerator is a multiple of $3$ and denominator is a multiple of $5$, so if we notice they are increasing in same order

So, next four are $\frac{-15}{25},\frac{-18}{30},\frac{-21}{35},\frac{-24}{40}$

ii) $\frac{-1}{4},\frac{-2}{8},\frac{-3}{12}...$

It can be observed, numerator are incremented by one and multiplied by $(-1)$

and denominator are multiple of $4$

So, next four are

$\frac{-4}{16},\frac{-5}{20},\frac{-6}{24},\frac{-7}{28}...$