Find the sum of the following $APs$: $0.6, 1.7, 2.8, \ldots,$ to $100$ terms.

$A$ 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?

The houses of a row are numbered consecutively from $1$ to $49$. Show that there is a value of $x$ such that the sum of the numbers of the houses preceding the house numbered $x$ is equal to the sum of the numbers of the houses following it. Find this value of $x$.

Find the sum of the first $51$ terms of an $AP$ whose second and third terms are $14$ and $18$ respectively.

Find the sum given below: $34 + 32 + 30 + \ldots + 10$

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 5 - 6n$. Find the sum of the first $n$ terms of the $A.P.$