Which of the following is NOT a property of geometric progressions?
Practice Questions
Q1
Which of the following is NOT a property of geometric progressions?
The product of the terms is equal to the square of the geometric mean.
The sum of the terms can be negative.
The common ratio can be zero.
The terms can be fractions.
Questions & Step-by-Step Solutions
Which of the following is NOT a property of geometric progressions?
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 properties of geometric progressions. These include: the common ratio is constant, the first term can be any number, and the common ratio cannot be zero.
Step 3: Analyze the question. It asks which option is NOT a property of geometric progressions.
Step 4: Recall that if the common ratio is zero, the sequence would not continue as a geometric progression, since multiplying by zero results in all subsequent terms being zero.
Step 5: Conclude that the common ratio cannot be zero is a true property of geometric progressions, and therefore, any option suggesting otherwise is NOT a property.
