Is (14,28,42,56,...) an arithmetic progression?

Yes, common difference is (14)

The governing concept is the constant-difference test for an arithmetic progression. Subtract consecutive terms: 28 − 14 = 14, 42 − 28 = 14, and 56 − 42 = 14. Since every difference is 14, the sequence is an arithmetic progression with common difference d = 14. Hence option A is correct. Option B mistakes the second term, 28, for the common difference. Option C is incorrect because an arithmetic progression need not have equal terms; it needs equal differences between consecutive terms. Option D is incorrect because the terms are increasing, not decreasing. The sequence can also be written using the nth-term rule aₙ = 14 + (n − 1)14, which reinforces that the same amount is added at each step. Equal consecutive differences are the decisive reason.

This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Arithmetic Progression.