For the $A.P.$ $100, 98, 96, 94, \ldots$,find the value of $a$.

The ratio of the sums of first $n$ terms of two $A.P.s$ is $(7n + 1) : (4n + 27)$. Find the ratio of their $m^{th}$ terms.

Four numbers in increasing order form an $A.P.$ The sum of those numbers is $32$ and the ratio of the product of extremes to the product of means is $7: 15$. Find those numbers.

Which term of the $A.P.$ $-1, 3, 7, 11, \ldots$ is $95$ (in $^{th}$)?

If the $n^{th}$ term of the $A.P.$ $9, 7, 5, \ldots$ and the $n^{th}$ term of the $A.P.$ $15, 12, 9, \ldots$ are equal,find the value of $n$.

For any $A.P.$,$T_{30} - T_{20} = \ldots \ldots \ldots \ldots$