Find the $n^{th}$ term of the $A.P. \, 6.4, 7.6, 8.8, 10, \ldots$

Find the number of terms in the finite $A.P.$ $7, 11, 15, \ldots, 107$.

Which term of the $A.P.$ $63, 65, 67, \ldots$ and $3, 10, 17, \ldots$ are equal (in $^{th}$)?

For a given $A.P.$,the $5^{th}$ term is $20$ and the $10^{th}$ term is $35$. Find the sum of the first $20$ terms of this $A.P.$

Let $S_n$,$S_{2n}$,and $S_{3n}$ be the sums of $n$,$2n$,and $3n$ terms of an Arithmetic Progression $(AP)$,respectively. Prove that $S_{3n} = 3(S_{2n} - S_n)$.

Which term of the $A.P. \, 53, 48, 43, \ldots$ is the first negative term?