If the common ratio of a GP is negative, which of the following statements is tr

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Question: If the common ratio of a GP is negative, which of the following statements is true?

Options:

Correct Answer: The terms will alternate in sign.

Solution:

In a GP with a negative common ratio, the terms will alternate in sign, starting from the sign of the first term.

If the common ratio of a GP is negative, which of the following statements is true?

If the common ratio of a GP is negative, which of the following statements is true?

Step 1: Understand what a GP (Geometric Progression) is. A GP is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed number called the common ratio.
Step 2: Identify what a negative common ratio means. A negative common ratio means that when you multiply a term by this ratio, the sign of the term will change.
Step 3: Start with the first term of the GP. If the first term is positive, the second term will be negative (because of the negative common ratio).
Step 4: Continue this pattern. The third term will be positive again (negative times negative equals positive), and the fourth term will be negative.
Step 5: Conclude that the terms will alternate in sign. If the first term is positive, the sequence will be positive, negative, positive, negative, and so on. If the first term is negative, the sequence will be negative, positive, negative, positive.

Geometric Progression (GP) – 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.
Common Ratio – The factor by which we multiply each term to get the next term in a geometric progression.
Sign Alternation – In a GP with a negative common ratio, the signs of the terms will alternate, starting with the sign of the first term.