For a given $A.P.$,$T_{7} = 12$ and $T_{12} = 72$. Then,$d = \dots \dots \dots \dots$

Determine the $AP$ whose fifth term is $19$ and the difference of the eighth term from the thirteenth term is $20$.

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: $1.4, 2.3, 3.2, 4.1, \dots$

Which of the following matchings is true for Part $I$ and Part $II$?

Part $I$	Part $II$
$1$. Sixth term of the $A.P.$ $1, 3, 5, 7, \ldots$	$a$. $105$
$2$. Eleventh term of the $A.P.$ $3, 6, 9, 12, \ldots$	$b$. $11$
$3$. Sixteenth term of the $A.P.$ $4, 6, 8, 10, \ldots$	$c$. $33$
$4$. Twenty-first term of the $A.P.$ $5, 10, 15, 20, \ldots$	$d$. $34$

The sum of the first $16$ terms of the $A.P.$ $1, 1.5, 2, \ldots$ is:

Find the sum of the integers between $100$ and $200$ that are not divisible by $9$.