Math Problem Statement

Determine whether the sequence is arithmetic, geometric or neither: 0.3, -3, 30, -300, 3000. If the sequence is geometric, what is the common ratio?

Solution

To determine if the sequence 0.3,3,30,300,30000.3, -3, 30, -300, 3000 \dots is arithmetic, geometric, or neither, let us analyze it step by step.


Step 1: Checking if the sequence is arithmetic

An arithmetic sequence has a constant difference between consecutive terms. To check this:

  1. 30.3=3.3-3 - 0.3 = -3.3
  2. 30(3)=3330 - (-3) = 33
  3. 30030=330-300 - 30 = -330

The differences are not constant ((-3.3, 33

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Math Problem Analysis

Mathematical Concepts

Arithmetic Sequences
Geometric Sequences

Formulas

Common difference: d = a(n) - a(n-1)
Common ratio: r = a(n) / a(n-1)

Theorems

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Suitable Grade Level

Grades 8-10