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

Which term of the $AP: 3, 15, 27, 39, \ldots$ will be $132$ more than its $54^{th}$ term?

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

$A$ 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 $10^{th}$ year.

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 $x$.

For the following $APs,$ write the first term and the common difference: $0.6, 1.7, 2.8, 3.9, \ldots$