Question

use inductive reasoning to predict the next three numbers in the pattern.

(9, 3, 1, \frac{1}{3}, \frac{1}{9}, \dots)

predict the next three numbers in the pattern.

(9, 3, 1, \frac{1}{3}, \frac{1}{9}), , ,

Explanation:

Analyze the given sequence

Using the Pattern Recognition and Sequences knowledge points

$$
LATEXBLOCK0
$$

Determine the pattern rule

Using the Inductive Reasoning knowledge point

$$
LATEXBLOCK1
$$

Each term is obtained by multiplying the previous term by \(\frac{1}{3}\).

Calculate the next three terms

Using the Sequences knowledge point

$$
LATEXBLOCK2
$$

Answer:

Predict the next three numbers in the pattern.

\(9, 3, 1, \frac{1}{3}, \frac{1}{9}\), <blank>\(\frac{1}{27}\)</blank>, <blank>\(\frac{1}{81}\)</blank>, <blank>\(\frac{1}{243}\)</blank>