Write four more numbers in the pattern: -1 3 , -2 6 , -3 9 , -4 1…

Question

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

✓

Answer

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 $\frac{-1 \times 5}{3 \times 5}=\frac{-5}{15}, \frac{-1 \times 6}{3 \times 6}=\frac{-6}{18}, \frac{-1 \times 7}{3 \times 7}=\frac{-7}{21}$

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