State whether the following sequence is an A.P. or not 13, 23, 33, 43, ....

i. State whether the following sequence is an A.P. or not 1³, 2³, 3³, 4³, ....

Answer. In order to check whether the given sequence is an A.P. or not we need to see the difference of any two consecutive terms of the sequence is same or not. If the difference is constant then it is an A.P. otherwise not.

Here,  t₁ = 1³ , t₂ = 2³ , t₃ = 3³ , t₄ = 4³

∴ t₂ – t₁ = 2³ - 1³ = 8 – 1 = 7

∴ t₃ – t₂ = 3³ – 2³ = 27 – 8 = 19

∴ t₄ – t₃ = 4³ – 3³ = 64 – 27 = 37

From above, the difference between any two consecutive term is not constant.

∴ the given sequence is not an A.P.