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