Do $1, 1, 1, 2, 2, 2, 3, 3, 3, \ldots$ form an $AP$? If they form an $AP$,write the next two terms.

(NO) An arithmetic progression $(AP)$ is a sequence of numbers such that the difference between any two consecutive terms is constant.
Let the sequence be $a_1, a_2, a_3, a_4, \ldots = 1, 1, 1, 2, 2, 2, 3, 3, 3, \ldots$
Calculate the common difference $d$ between consecutive terms:
$d_1 = a_2 - a_1 = 1 - 1 = 0$
$d_2 = a_3 - a_2 = 1 - 1 = 0$
$d_3 = a_4 - a_3 = 2 - 1 = 1$
Since $d_1 = d_2 \neq d_3$,the difference between consecutive terms is not constant.
Therefore,the given sequence does not form an $AP$.