Which of the following statements about geometric progressions is true?

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

Options:

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 geometric progressions is true?

Which of the following statements about geometric progressions 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 geometric progressions. The ratio of any two consecutive terms in the sequence is always the same.
Step 3: For example, in the sequence 2, 6, 18, 54, the common ratio is 3 because 6/2 = 3, 18/6 = 3, and 54/18 = 3.
Step 4: Conclude that the statement about the constant ratio of consecutive terms is true for geometric progressions.

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