Which term of the $AP : 3, 8, 13, 18, \ldots$ is $78$ (in $^{th}$)?

$A$ manufacturer of $TV$ sets produced $600$ sets in the third year and $700$ sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year,find the production in the $1^{st}$ year.

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

Write the first four terms of the $AP,$ when the first term $a$ and the common difference $d$ are given as follows: $a = -1, d = \frac{1}{2}$

Subba Rao started work in $1995$ at an annual salary of ₹ $5000$ and received an increment of ₹ $200$ each year. In which year did his income reach ₹ $7000$?

$A$ 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?