Question

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

3n² + 5

Answer 1

No. Here a_n = 3n² + 5

Put n = 1, a₁ = 3(1)² + 5 = 8

Put n = 2, a₂ = 3(2)² + 5 = 3(4) + 5 = 17

Put n = 3, a₁ = 3(3)² + 5 = 3(9) + 5 = 27 + 5 = 32

So, the list of number becomes 8, 17, 32,….

Here, a₂ – a₁ = 17 – 8 = 9

a₃ – a₂ = 32 -17 = 15

∴ a₂ – a₁ ≠ a₃ – a₂

Since the difference of the successive term is not same.

So, it does not form an AP.