If z, 5z, 25z, ... is a geometric progression, what is the common ratio?
Answer and explanation
Correct answer: 5
The governing concept remains the quotient of consecutive terms, and algebraic symbols may be simplified in exactly the same way as numbers. Divide the second term by the first: r = 5z ÷ z = 5, assuming z is nonzero as required for this quotient. The next check gives 25z ÷ 5z = 5, confirming that the ratio is constant. Therefore option B is correct. Option A is the first algebraic term, not the multiplier between terms. Option C is the third coefficient or third displayed term’s coefficient, while option D is an unrelated product. The variable cancels because it is a common nonzero factor.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The governing concept remains the quotient of consecutive terms, and algebraic symbols may be simplified in exactly the same way as numbers. Divide the second term by the first: r = 5z ÷ z = 5, assuming z is nonzero as required for this quotient. The next check gives 25z ÷ 5z = 5, confirming that the ratio is constant. Therefore option B is correct. Option A is the first algebraic term, not the multiplier between terms. Option C is the third coefficient or third displayed term’s coefficient, while option D is an unrelated product. The variable cancels because it is a common nonzero factor.
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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