If \((y,4y,16y,\ldots)\) is a geometric progression, what is the common ratio?
Answer and explanation
Correct answer: \(4\)
A geometric progression is defined by a constant ratio between every pair of consecutive terms. Divide the second term by the first term: \(r=\frac{4y}{y}=4\), provided the first term is nonzero, as is understood in this sequence. The check using the next pair gives \(\frac{16y}{4y}=4\) as well, confirming that the ratio is constant. Thus option C is correct. Option B could arise from noticing that 4 is twice 2, but it is not the multiplier between consecutive terms. Options A and D likewise do not transform \(y\) into \(4y\).
Frequently asked questions
What is the correct answer to this question?
\(4\)
Why is this the correct answer?
A geometric progression is defined by a constant ratio between every pair of consecutive terms. Divide the second term by the first term: \(r=\frac{4y}{y}=4\), provided the first term is nonzero, as is understood in this sequence. The check using the next pair gives \(\frac{16y}{4y}=4\) as well, confirming that the ratio is constant. Thus option C is correct. Option B could arise from noticing that 4 is twice 2, but it is not the multiplier between consecutive terms. Options A and D likewise do not transform \(y\) into \(4y\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Geometric Progression.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
