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=(-54)/(18)=(18)/(-6)=(-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