Check whether $301$ is a term of the list of numbers $5, 11, 17, 23, \ldots$

$-10, -6, -2, 2, \ldots$ are $APs$? If they form an $AP$,find the common difference $d$ and write three more terms.

In an $AP$ given $a=5, d=3, a_{n}=50,$ find $n$ and $S_{n}$.

If the sum of the first $n$ terms of an $AP$ is $4n - n^2$,what is the first term (that is $S_1$)? What is the sum of first two terms? What is the second term? Similarly,find the $3^{rd}$,the $10^{th}$ and the $n^{th}$ terms.

$A$ sum of ₹ $1000$ is invested at $8 \%$ simple interest per year. Calculate the interest at the end of each year. Do these interests form an $AP$? If so,find the interest at the end of $30 \text{ years}$ making use of this fact. (in ₹)

$A$ contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ $200$ for the first day,₹ $250$ for the second day,₹ $300$ for the third day,etc. The penalty for each succeeding day is ₹ $50$ more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by $30$ days?