Math Problem Statement

Examine the number patterns below, and determine whether or not they are linear in nature.

Solution

In this activity, we need to determine if the given patterns are linear or not. Let's examine each pattern individually:

  1. Pattern 1: 5, 15, 45, 135

    • This pattern does not increase by a constant difference but rather appears to increase by a common ratio (multiplying by 3 each time: 5×3=155 \times 3 = 15, 15×3=4515 \times 3 = 45, etc.).
    • Therefore, this is not a linear pattern (answer: N).
  2. Pattern 2: 1.2, 1.5, 1.8, 2.1

    • Here, each term increases by a constant difference of 0.3 (1.5 - 1.2 = 0.3, 1.8 - 1.5 = 0.3, etc.).
    • This is a linear pattern (answer: Y).
  3. Pattern 3: 105, 100, 96, 92

    • In this pattern, each term decreases by a constant difference of 5 (105 - 100 = 5, 100 - 96 = 4, 96 - 92 = 4).
    • This is a linear pattern

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear and Non-linear Patterns
Arithmetic Sequence
Geometric Sequence

Formulas

Constant difference for linear patterns
Constant ratio for geometric sequences

Theorems

Linear relationships have a constant rate of change

Suitable Grade Level

Grade 8