Is the sequence (5, 25, 125, 625, ...) a geometric progression?
Answer and explanation
Correct answer: Yes, its common ratio is 5
A sequence is a geometric progression when the ratio of every term to the immediately preceding term is constant. Check the consecutive ratios here: 25/5 = 5, 125/25 = 5, and 625/125 = 5. Since all these ratios are equal, the sequence is a geometric progression with common ratio 5. Therefore, option A is correct. The number 25 is a term of the sequence, not the common ratio, so option B confuses a term with a multiplier. Option C is contradicted by the equal ratios, and option D is false because the terms increase from 5 to 625 rather than decrease. The defining test is equal consecutive ratios.
Frequently asked questions
What is the correct answer to this question?
Yes, its common ratio is 5
Why is this the correct answer?
A sequence is a geometric progression when the ratio of every term to the immediately preceding term is constant. Check the consecutive ratios here: 25/5 = 5, 125/25 = 5, and 625/125 = 5. Since all these ratios are equal, the sequence is a geometric progression with common ratio 5. Therefore, option A is correct. The number 25 is a term of the sequence, not the common ratio, so option B confuses a term with a multiplier. Option C is contradicted by the equal ratios, and option D is false because the terms increase from 5 to 625 rather than decrease. The defining test is equal consecutive ratios.
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.
