Question

Justify whether it is true to say that `-1, - 3/2, -2, 5/2, .....` forms an AP as a₂ – a₁ = a₃ – a₂.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

a₁ = `-1`, a₂ = `-3/2`, a₃ = `-2` and a₄ = `5/2`

a₂ – a₁ = `-3/2 - (-1) = - 1/2`

a₃ – a₂ = `- 2 - (-3/2) = -1/2`

a₄ – a₃ = `5/2 - (-2) = 9/2`

Clearly, the difference of successive terms in not same

All though, a₂ – a₁ = a₃ – a₂ but a₄ – a₃ ≠ a₃ – a₂ 

Therefore it does not form an AP.