If the common ratio of a GP is negative, which of the following statements is tr
Practice Questions
Q1
If the common ratio of a GP is negative, which of the following statements is true?
The terms will always be positive.
The terms will alternate in sign.
The sum of the terms will be negative.
The first term must be negative.
Questions & Step-by-Step Solutions
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.
