Yasmin looked at the pattern 2, 6, 18, 54, and determined that the next number should be 162. What type of reasoning did she use?

A. inductive reasoning B. deductive reasoning C. algebraic reasoning D. direct reasoning

Jun 16, 2018

I would suggest B - deductive reasoning.

Explanation:

I would suggest B - deductive reasoning.

You look for relationships between the numbers.

If you do something to one number you get the next one.
This is most likely Arithmetic or Geometric sequence.

Arithmetic is derived by adding a constant value to one to get the next

Geometric is derived by multiplying by a constant.

Lest test for geometric:

I am going to divide each value by the one that preceded it.

$\frac{6}{2} = 3$

$\frac{18}{6} = 3$

$\frac{54}{18} = 3$

This is a geometric sequence as the division produces the same value each time.

Therefor $\frac{x}{54} = 3 \textcolor{w h i t e}{\text{d") =>color(white)("d")x=3xx54color(white)("d")=color(white)("d}} 162$ as required