Question

Your friend says that they can create a pattern in which the 100th image will have 102 shapes in it. Explain why you agree or disagree. Use images, patterns, or mathematical rules to justify your explanation.

A) I agree because the pattern shows a consistent increase in the number of shapes.
B) I disagree because the pattern does not follow a logical mathematical rule.
C) I agree because the pattern shows a steady progression.
D) I disagree because the pattern is not well-defined.

Answer 1

To determine whether the friend can create a pattern with 102 shapes in the 100th image, analyze the pattern for a consistent increase. If there is a steady progression, the claim is supported. If the pattern doesn't follow a logical rule or is not well-defined, the claim is contradicted.

Step-by-step explanation:

To determine whether your friend can create a pattern in which the 100th image will have 102 shapes, you need to analyze the pattern and look for a consistent increase in the number of shapes. If the pattern shows a steady progression, it would support your friend's claim. However, if the pattern does not follow a logical mathematical rule or is not well-defined, it would contradict their claim.

For example, if we have a pattern where each image has 2 more shapes than the previous one, we can observe that:

1. The 1st image has 1 shape.
2. The 2nd image has 3 shapes.
3. The 3rd image has 5 shapes.
4. The 4th image has 7 shapes.

Based on this pattern, we can infer that the 100th image would have 199 shapes, not 102.