Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1, d = \frac{1}{2}$

The houses of a row are numbered consecutively from $1$ to $49$. Show that there is a value of $x$ such that the sum of the numbers of the houses preceding the house numbered $x$ is equal to the sum of the numbers of the houses following it. Find this value of $x$.

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

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = 10, d = 10.$

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 $a, a^{2}, a^{3}, a^{4}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write three more terms.