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


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