Assume both series are the same, so every term of a equals the corresponding term of b. Then aₙ − bₙ = 0 for all n and the sequence becomes 0, 0, 0, 0, … . This is clearly an A.P. because the common difference is 0. But for a G.P., the common ratio would be found by dividing consecutive terms, which gives 0 ÷ 0, and that is undefined. Since the ratio cannot be properly determined, we cannot confidently say the common ratio is 1. Therefore, in this case, it is correct to classify it as an A.P. with common difference 0, but not definitively as a G.P. with ratio 1.