Question

Justify whether it is true to say that the 3n² + 5 are the nth terms of an AP.

Answer 1

Put n = 1, 2, 3, 4

We get

a₁ = 3(1)² + 5 = 8

a₂ = 3(2)² + 5 = 17

a₃ = 3(3)² + 5 = 32

a₄ = 3(4)² + 5 = 53

List of AP is 8, 17, 32, 53. . . .

a₂ - a₁ = 17 - 8 = 9

a₃ - a₂ = 32 - 17 = 15

As a₃ - a₂ is not equal to a₂ - a₁ the list is not an AP.