Question

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

1 + n + n²

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Here,

a_n = 1 + n + n²

Put n = 1,

a₁ = 1 + 1 + (1)² 

= 3

Put n = 2,

a₂ = 1 + 2 + (2)² 

= 1 + 2 + 4

= 7

Put n = 3,

a₃ = 1 + 3 + (3)²

= 1 + 3 + 9

= 13

So, the list of number becomes 3, 7, 13,...

Here, a₂ – a₁ = 7 – 3 = 4

a₃ – a₂ = 13 – 7 = 6

∴ a₂ – a₁ ≠ a₃ – a₂

Since, the difference of the successive term is not same.

So it does not form an AP.