In an $AP$ given $a=5, d=3, a_{n}=50,$ find $n$ and $S_{n}$.

Fill in the blanks in the following table,given that $a$ is the first term,$d$ is the common difference,and $a_{n}$ is the $n^{th}$ term of the $AP$:

$S.No.$	$a$	$d$	$n$	$a_{n}$
$(i)$	$7$	$3$	$8$	$...$
$(ii)$	$-18$	$...$	$10$	$0$
$(iii)$	$...$	$-3$	$18$	$-5$
$(iv)$	$-18.9$	$2.5$	$...$	$3.6$
$(v)$	$3.5$	$0$	$105$	$...$

Find the sum of:
$(i)$ the first $1000$ positive integers
$(ii)$ the first $n$ positive integers

$A$ manufacturer of $TV$ sets produced $600$ sets in the third year and $700$ sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year,find the production in the $10^{th}$ year.

Find the sum of the following $APs$ $-37, -33, -29, \ldots$ to $12$ terms.

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1.25, d = -0.25.$