Given, a1, а2, а3, ....... and b1, b2, b3, ....... are real numbers such that a1 – b1 = a2 – b2 = a3 – b3 = .......... are all equal. a1 – b1, a2 – b2, a3 – b3 .......... forms a ______ progression.

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Given, a1, а2, а3, ....... and b1, b2, b3, ....... are real numbers such that a1 – b1 = a2 – b2 = a3 – b3 = .......... are all equal. a1 – b1, a2 – b2, a3 – b3 .......... forms a arithmetic (d = 0) progression. Explanation: a1 – b1 = a2 – b2 = a3 – b3 = ... = c so the sequence of differences is constant every term = c. A constant sequence is an arithmetic progression with common difference d = 0. It is also a geometric progression with common ratio r = 1. When the common term is nonzero, the zero constant sequence is the degenerate case.

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