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

a, 2a + 1, 3a + 2, 4a + 3, …

Here a₁ = a

a₂ = 2a + 1

a₃ = 3a + 2

a₄ = 4a + 3

a₂ - a₁ = a + 1

a₃ - a₂ = a + 1

a₄ - a₃ = a + 1

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

next three term will be

4a + 3 + a + 1, 4a + 3 + 2(a + 1), 4a + 3 + 3(a + 1)

5a + 4, 6a + 5, 7a + 6