What is the value of r in the geometric progression (10, 40, 160, 640, …)?
Answer and explanation
Correct answer: 4
The governing concept is the common ratio of a geometric progression. It is found by dividing any term by the immediately preceding term. Using the first two terms, r = 40 ÷ 10 = 4. The result is verified by the next pairs: 160 ÷ 40 = 4 and 640 ÷ 160 = 4. Therefore, option B is correct. Option A is too small and does not produce 40 from 10; option C would produce 80 from 10; and option D would produce 100 from 10. The fact that the first term is 10 is not itself the value of r. Consistent division between consecutive terms is the required test.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is the common ratio of a geometric progression. It is found by dividing any term by the immediately preceding term. Using the first two terms, r = 40 ÷ 10 = 4. The result is verified by the next pairs: 160 ÷ 40 = 4 and 640 ÷ 160 = 4. Therefore, option B is correct. Option A is too small and does not produce 40 from 10; option C would produce 80 from 10; and option D would produce 100 from 10. The fact that the first term is 10 is not itself the value of r. Consistent division between consecutive terms is the required test.
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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