Justify whether it is true to say that the following are the nth terms of an AP.
1 + n + n²

Question

Justify whether it is true to say that the following are the nth terms of an AP. 1 + n + n 2

Philoid · Accepted Answer

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

Justify whether it is true to say that the following are the nth terms of an AP.1 + n + n2