Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $1, 4, 9, 16, \ldots $

(N/A) To determine if the sequence $1, 4, 9, 16, \ldots$ is an $A.P.$,we check the difference between consecutive terms.
Let the sequence be $a_1, a_2, a_3, a_4, \ldots$ where $a_1 = 1, a_2 = 4, a_3 = 9, a_4 = 16$.
The difference $d_1 = a_2 - a_1 = 4 - 1 = 3$.
The difference $d_2 = a_3 - a_2 = 9 - 4 = 5$.
Since $d_1 \neq d_2$,the common difference is not constant.
Therefore,the sequence $1, 4, 9, 16, \ldots$ is not an $A.P.$