Why is 3, 7, 13, 21, … not an arithmetic progression?
Answer and explanation
Correct answer: Because consecutive differences are not equal
An arithmetic progression is defined by a constant difference between every pair of consecutive terms. For this sequence, the differences are 7 − 3 = 4, 13 − 7 = 6, and 21 − 13 = 8. Since 4, 6, and 8 are not equal, the sequence does not satisfy the defining condition. Therefore option C is correct. The first term may be any number, and positive terms can certainly form an arithmetic progression, so A and B are irrelevant. An infinite progression does not need a final term, so D is also incorrect. The terms increase, but mere increase is not enough; the amount of increase must remain constant.
Frequently asked questions
What is the correct answer to this question?
Because consecutive differences are not equal
Why is this the correct answer?
An arithmetic progression is defined by a constant difference between every pair of consecutive terms. For this sequence, the differences are 7 − 3 = 4, 13 − 7 = 6, and 21 − 13 = 8. Since 4, 6, and 8 are not equal, the sequence does not satisfy the defining condition. Therefore option C is correct. The first term may be any number, and positive terms can certainly form an arithmetic progression, so A and B are irrelevant. An infinite progression does not need a final term, so D is also incorrect. The terms increase, but mere increase is not enough; the amount of increase must remain 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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