Find the $n^{th}$ term of the $A.P. \, 18, 16.5, 15, 13.5, \ldots$

From natural numbers $1$ to $288,$ find the number $x$ such that the sum of all natural numbers smaller than $x$ is equal to the sum of all natural numbers greater than $x$ but less than or equal to $288.$

For a given $A.P.$,the $11^{th}$ term is $38$ and the $16^{th}$ term is $73$. Find the $31^{st}$ term of the $A.P.$

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = 10 - 6n$. Find the sum of the first $n$ terms of the $A.P.$

Find the sum of the first $20$ terms of the $A.P.$ $50, 46, 42, \ldots$

For a given $A.P.$,$S_{20} = 100$ and $d = -2$. Then,$a = \ldots$