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Which of the following statements about a geometric progression is true?

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Question: Which of the following statements about a geometric progression is true?

Options:

  1. The ratio of consecutive terms is constant.
  2. The difference between consecutive terms is constant.
  3. The sum of the terms is always positive.
  4. The first term is always the largest.

Correct Answer: The ratio of consecutive terms is constant.

Solution:

In a geometric progression, the ratio of consecutive terms is indeed constant, which defines the progression.

Which of the following statements about a geometric progression is true?

Practice Questions

Q1
Which of the following statements about a geometric progression is true?
  1. The ratio of consecutive terms is constant.
  2. The difference between consecutive terms is constant.
  3. The sum of the terms is always positive.
  4. The first term is always the largest.

Questions & Step-by-Step Solutions

Which of the following statements about a geometric progression is true?
  • Step 1: Understand what a geometric progression is. It is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
  • Step 2: Identify the key property of a geometric progression. The ratio of any term to the term before it is always the same (constant).
  • Step 3: Recognize that this constant ratio is what defines the geometric progression.
  • Step 4: Conclude that the statement about the ratio of consecutive terms being constant is true for geometric progressions.
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