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)