The $21^{\text{st}}$ term of the $AP$ whose first two terms are $-3$ and $4$ is

For an $A.P.$,the $2^{nd}$ term is $2$ and the $7^{th}$ term is $22$. Find the sum of the first $30$ terms of the $A.P.$

The sum of all the terms of a finite $A.P.$ having $n$ terms is given by $S_{n} = \ldots \ldots \ldots$

The ratio of the $11^{\text{th}}$ term to the $18^{\text{th}}$ term of an $AP$ is $2:3$. Find the ratio of the $5^{\text{th}}$ term to the $21^{\text{st}}$ term,and also the ratio of the sum of the first five terms to the sum of the first $21$ terms.

The production of a $TV$ factory increases equally every year. Its production in the $3^{rd}$ year was $600 \, TV$ and its production in the $7^{th}$ year was $700 \, TV$. Find the production in the $1^{st}$ year,in the $10^{th}$ year,and the total production in $7$ years.

If the $n^{th}$ term of the $A.P.$ $9, 7, 5, \ldots$ and the $n^{th}$ term of the $A.P.$ $15, 12, 9, \ldots$ are equal,find the value of $n$.