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
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)
3