Which of the following statements about geometric progressions is true?
Practice Questions
Q1
Which of the following statements about geometric progressions is true?
The ratio of consecutive terms is constant.
The sum of terms is always positive.
The first term must be greater than the second.
The common ratio can only be an integer.
Questions & Step-by-Step Solutions
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.
