If the consecutive differences of a sequence are (2,4,6), what is the correct conclusion?

It is not an arithmetic progression

For a sequence to be an arithmetic progression, the difference between every pair of consecutive terms must be one constant number. It is not enough for the terms to increase, decrease, or have one matching difference. The test must be applied to all consecutive differences that are provided.

Here the consecutive differences are listed as 2, 4, and 6. Because these numbers are not equal, there is no single constant common difference. Therefore the sequence is not an arithmetic progression, which makes choice B correct. Choice C is not correct because 2 is only the first difference, not the common difference of the whole sequence. Equal terms would instead give difference 0, and that is not the situation here.

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..