Which of the following is a decreasing arithmetic progression?
Answer and explanation
Correct answer: (50,45,40,35,\ldots)
A decreasing arithmetic progression must have a constant negative common difference. In option A, the consecutive differences are 45 − 50 = −5, 40 − 45 = −5, and 35 − 40 = −5. Both conditions are satisfied: the terms decrease and the difference remains constant, so option A is correct. Option B doubles each time, giving a constant ratio rather than a constant difference, so it is geometric. Option C has common difference 0, so it is constant, not decreasing. Option D contains successive squares, whose differences are 3, 5, and 7, so the difference is not constant.
Frequently asked questions
What is the correct answer to this question?
(50,45,40,35,\ldots)
Why is this the correct answer?
A decreasing arithmetic progression must have a constant negative common difference. In option A, the consecutive differences are 45 − 50 = −5, 40 − 45 = −5, and 35 − 40 = −5. Both conditions are satisfied: the terms decrease and the difference remains constant, so option A is correct. Option B doubles each time, giving a constant ratio rather than a constant difference, so it is geometric. Option C has common difference 0, so it is constant, not decreasing. Option D contains successive squares, whose differences are 3, 5, and 7, so the difference is not constant.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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