Which of the following is NOT a property of a geometric progression?

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Question: Which of the following is NOT a property of a geometric progression?

Options:

The product of the first and last terms equals the square of the geometric mean.
The sum of the terms can be negative.
The ratio of the last term to the first term is equal to the common ratio raised to the power of (n-1).
The terms can be non-numeric.

Correct Answer: The terms can be non-numeric.

Solution:

In a geometric progression, the terms are numeric and follow a specific ratio; thus, non-numeric terms do not form a valid GP.

Which of the following is NOT a property of a geometric progression?

The product of the first and last terms equals the square of the geometric mean.
The sum of the terms can be negative.
The ratio of the last term to the first term is equal to the common ratio raised to the power of (n-1).
The terms can be non-numeric.

Which of the following is NOT a property of a geometric progression?

Step 1: Understand what a geometric progression (GP) is. A GP 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 properties of a geometric progression. The main properties include: all terms are numeric, the ratio between consecutive terms is constant, and the sequence can be finite or infinite.
Step 3: Consider what would not be a property of a GP. Since a GP consists of numbers, any sequence that includes non-numeric terms (like letters or symbols) cannot be a GP.
Step 4: Conclude that the presence of non-numeric terms is NOT a property of a geometric progression.

No concepts available.