For the $A.P.$ $100, 98, 96, 94, \ldots$,find the value of $a$.

Are $\sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32}, \ldots$ in an $AP$? If they form an $AP$,find the common difference $d$ and write the next three terms.

Write the first three terms of the $APs$ when $a$ and $d$ are as given below:
$a = -5, d = -3$

For the following $APs$,write the first term and the common difference: $\frac{1}{3}, \frac{5}{3}, \frac{9}{3}, \frac{13}{3}, \ldots$

The sum of four numbers in $A.P.$ is $50$. The greatest number is four times the smallest number. Find those numbers.

The taxi fare after each $km$ when the fare is ₹ $15$ for the first $km$ and ₹ $8$ for each additional $km$. Does the list of numbers involved form an arithmetic progression,and why?