Question

use inductive reasoning to predict the next three numbers in the pattern.
3, -12, 48, -192, ...

predict the next three numbers in the pattern.
3, -12, 48, -192, \\(\square\\), \\(\square\\), \\(\square\\)

Explanation:

Step1: Identify the pattern

Check the ratio between consecutive terms: $\frac{-12}{3} = -4$, $\frac{48}{-12} = -4$, $\frac{-192}{48} = -4$. Each term is multiplied by $-4$ to get the next term.

Step2: Calculate 5th term

Multiply the 4th term by $-4$: $-192 \times (-4) = 768$

Step3: Calculate 6th term

Multiply the 5th term by $-4$: $768 \times (-4) = -3072$

Step4: Calculate 7th term

Multiply the 6th term by $-4$: $-3072 \times (-4) = 12288$

Answer:

768, -3072, 12288