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

Question

Verify that each of the following is an AP and then write its next three terms. a, 2a + 1, 3a + 2, 4a + 3, …

Philoid · Accepted Answer

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