For the following $APs$,$-5, -1, 3, 7, \ldots$,write the first term and the common difference.

Show that $a_{1}, a_{2}, \ldots, a_{n}, \ldots$ form an $AP$ where $a_{n}$ is defined as $a_{n}=3+4 n$. Also,find the sum of the first $15$ terms.

$200$ logs are stacked in the following manner: $20$ logs in the bottom row,$19$ in the next row,$18$ in the row next to it and so on (see Figure). In how many rows are the $200$ logs placed and how many logs are in the top row?

Find the $10^{th}$ term of the $AP : 2, 7, 12, \ldots$

Find the sum of the odd numbers between $0$ and $50$.

Find the sum given below: $-5 + (-8) + (-11) + \ldots + (-230)$