$a, 2a, 3a, 4a, \dots$ are $APs$? If they form an $AP,$ find the common difference $d$ and write three more terms.

Find the sum of first $22$ terms of an $AP$ in which $d=7$ and $22^{nd}$ term is $149$.

Find the $20^{th}$ term from the last term of the $AP : 3, 8, 13, \ldots, 253.$

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

In which of the following situations,does the list of numbers involved make an arithmetic progression,and why? The amount of money in the account every year,when ₹ $10000$ is deposited at compound interest at $8 \%$ per annum.

$A$ 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?