Question

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

3n² + 5

Options

• True

• False

Answer 1

This statement is False.

Explanation:

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.