In an $AP$ if $a = -7.2, d = 3.6, a_{n} = 7.2,$ then $n$ is

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 $A.P.$ $5, 10, 15, 20, \ldots$	$d$. $34$

If the $9^{\text{th}}$ term of an $AP$ is zero,prove that its $29^{\text{th}}$ term is twice its $19^{\text{th}}$ term.

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: $5, 11, 17, 23, \ldots$

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 4n + 7$. Find the sum of $n$ terms of this $A.P.$

To clear a debt,Ajaybhai has to pay $Rs. 100$ in the first monthly instalment,$Rs. 150$ in the second monthly instalment,and onwards he has to pay in each monthly instalment $Rs. 50$ more than what was paid in the previous instalment. He has to pay $24$ monthly instalments in all. What amount will he pay in the $24^{th}$ instalment?