Verify that each of the following is an AP and then write its next three terms.

a + b, (a + 1) + b, (a + 1) + (b + 1), …


Here


a1 = a + b


a2 = (a + 1) + b


a3 = (a + 1) + (b + 1)


a2 - a1 = (a + 1) + b - (a + b) = 1


a3 - a2 = (a + 1) + (b + 1) - (a + 1) - b = 1


as difference of successive terms are equal therefore its an AP with common difference


next three term will be


(a + 1) + (b + 1) + 1, (a + 1) + (b + 1) + 1(2), (a + 1) + (b + 1) + 1(3)


(a + 2) + (b + 1), (a + 2) + (b + 2), (a + 3) + (b + 2)


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