How many terms of the $AP: 24, 21, 18, \ldots$ must be taken so that their sum is $78$?

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 $AP$:

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

Are $3, 3+\sqrt{2}, 3+2\sqrt{2}, 3+3\sqrt{2}, \ldots$ in $AP$? If they form an $AP$,find the common difference $d$ and write the next three terms.

$A$ sum of ₹ $700$ is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is ₹ $20$ less than its preceding prize,find the value of each of the prizes.

In an $AP$,given $a=2, d=8, S_{n}=90$,find $n$ and $a_{n}$.

In an $AP$,given $d=5$ and $S_{9}=75$,find $a$ and $a_{9}$.