In which sequence are the first three consecutive differences (4, 4, 4)?
Answer and explanation
Correct answer: (2, 6, 10, 14, ...)
The governing concept is the common difference of an arithmetic progression. For option A, subtract consecutive terms: 6−2=4, 10−6=4, and 14−10=4. Thus its first three consecutive differences are exactly (4,4,4), and it is an arithmetic progression with common difference 4. In option B the differences are 4, 5, and 6, so they change. In option C each difference is −2, not +4. In option D the differences are 3, 5, and 7, which also are not constant. Hence only option A satisfies the stated condition. The repeated wording in the supplied option has been normalized, without changing the mathematical choices or answer.
Frequently asked questions
What is the correct answer to this question?
(2, 6, 10, 14, ...)
Why is this the correct answer?
The governing concept is the common difference of an arithmetic progression. For option A, subtract consecutive terms: 6−2=4, 10−6=4, and 14−10=4. Thus its first three consecutive differences are exactly (4,4,4), and it is an arithmetic progression with common difference 4. In option B the differences are 4, 5, and 6, so they change. In option C each difference is −2, not +4. In option D the differences are 3, 5, and 7, which also are not constant. Hence only option A satisfies the stated condition. The repeated wording in the supplied option has been normalized, without changing the mathematical choices or 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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