Choose the correct choice in the following and justify: $30^{th}$ term of the $AP: 10, 7, 4, \ldots$ is

In the following $APs,$ find the missing terms in the boxes: $\square, 38, \square, \square, \square, -22$

For the following $APs,$ write the first term and the common difference: $0.6, 1.7, 2.8, 3.9, \ldots$

The cost of digging a well after every metre of digging, when it costs ₹ $150$ for the first metre and rises by ₹ $50$ for each subsequent metre, does the list of numbers involved make an arithmetic progression, and why?

In an $AP$ given $a=7$ and $a_{13}=35$,find $d$ and $S_{13}$.

$A$ 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.