Justify whether it is true to say that the following are the nth terms of an AP.

1 + n + n2

Put n = 1, 2, 3, 4


We get


a1 = 1 + 1 + (1)2 = 3


a2 = 1 + 2 + (2)2 = 7


a3 = 1 + 3 + (3)2 = 13


a4 = 1 + 4 + (4)2 = 21


List of AP is 3, 7, 13, 21. . . .


a2 - a1 = 7 - 3 = 4


a3 - a2 = 13 - 7 = 6


As


a3 - a2 is not equal to a2 - a1


the list is not an AP


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