Question

Write four more numbers in the following pattern-
$\frac{-1}{3}$, $\frac{-2}{6}$, $\frac{-3}{9}$, $\frac{-4}{12}$..........

Answer 1

We have
$\frac{-2}{6}$= $\frac{-1\times 2}{3\times 2}$
$\frac{-3}{9}$= $\frac{-1\times 3}{3\times 3}$
$\frac{-4}{12}$=$\frac{-1\times 4}{3\times 4}$
or $\frac{-1\times 1}{3\times 1}$ = $\frac{-1}{3}$
$\frac{-1\times 2}{3\times 2}$ = $\frac{-2}{6}$
$\frac{-1\times 3}{3\times 3}$ = $\frac{-3}{9}$
$\frac{-1\times 4}{3\times 4}$ = $\frac{-4}{12}$
Thus we observe a pattern in these numbers
The other numbers would be $\frac{-1\times 5}{3\times 5}$ = $\frac{-5}{15}$,
$\frac{-1\times 6}{3\times 61}$ = $\frac{-6}{18}$,$\frac{-1\times 1}{3\times 7}$ = $\frac{-7}{21}$