Is (10,20,40,80,\ldots) a geometric progression?
Answer and explanation
Correct answer: Yes, common ratio is (2)
A sequence is a geometric progression when the ratio of every term to the term immediately before it is constant. The terms do not need to be equal; instead, they are repeatedly multiplied by the same number. This constant number is called the common ratio.
For the given sequence, \(20\div10=2\), \(40\div20=2\), and \(80\div40=2\). Since all consecutive ratios are equal to 2, the sequence is a geometric progression with common ratio 2. Therefore, option A is correct. The value 10 is the first term, not the ratio, and the sequence is increasing rather than decreasing.
Frequently asked questions
What is the correct answer to this question?
Yes, common ratio is (2)
Why is this the correct answer?
A sequence is a geometric progression when the ratio of every term to the term immediately before it is constant. The terms do not need to be equal; instead, they are repeatedly multiplied by the same number. This constant number is called the common ratio.
For the given sequence, \(20\div10=2\), \(40\div20=2\), and \(80\div40=2\). Since all consecutive ratios are equal to 2, the sequence is a geometric progression with common ratio 2. Therefore, option A is correct. The value 10 is the first term, not the ratio, and the sequence is increasing rather than decreasing.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
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