For the $A.P.$ $0.1, 0.4, 0.7, 1, \ldots,$ the common difference is.........

Determine the $AP$ whose fifth term is $19$ and the difference of the eighth term from the thirteenth term is $20$.

The sum of the first $n$ terms of an $AP$ whose first term is $8$ and the common difference is $20$ is equal to the sum of first $2n$ terms of another $AP$ whose first term is $-30$ and the common difference is $8$. Find $n$.

How many numbers lie between $10$ and $300,$ which when divided by $4$ leave a remainder $3?$

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

If the numbers $n-2, 4n-1$ and $5n+2$ are in $AP$,find the value of $n$.