Which sequence is an arithmetic progression with common difference −7?
Answer and explanation
Correct answer: (49, 42, 35, 28, …)
To identify the required arithmetic progression, subtract each term from the following term and check whether every result is −7. In option A, 42 − 49 = −7, 35 − 42 = −7, and 28 − 35 = −7. Thus the terms decrease by exactly 7 at every step, so option A satisfies the condition. Option B has common difference +7, option C has common difference −9 because 40 − 49 = −9, and option D has common difference +7. A negative common difference means that the sequence decreases as it proceeds; it does not require the terms themselves to be negative. Therefore option A is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
(49, 42, 35, 28, …)
Why is this the correct answer?
To identify the required arithmetic progression, subtract each term from the following term and check whether every result is −7. In option A, 42 − 49 = −7, 35 − 42 = −7, and 28 − 35 = −7. Thus the terms decrease by exactly 7 at every step, so option A satisfies the condition. Option B has common difference +7, option C has common difference −9 because 40 − 49 = −9, and option D has common difference +7. A negative common difference means that the sequence decreases as it proceeds; it does not require the terms themselves to be negative. Therefore option A is the only correct answer.
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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