Question

use inductive reasoning to predict the next three numbers in the pattern. 2, -6, 18, -54______

Answer 1

Given the pattern:

$2,-6,18,-54,\ldots\ldots$

The given pattern is geometric sequence

The first term is = a = 2

The common ratio = r

$r=\frac{-54}{18}=\frac{18}{-6}=\frac{-6}{2}=-3$

So, the next three numbers will be :

$\begin{gathered} -54\cdot-3=162 \\ \\ 162\cdot-3=-486 \\ \\ -486\cdot-3=1458 \end{gathered}$

So, the answer is : the next three numbers are : 162 , -486 , 1458