If $x, y, z$ are three consecutive terms of an $A.P.$,then the common difference of the $A.P.$ is........

Yasmeen saves $Rs.\, 32$ during the first month,$Rs.\, 36$ in the second month,and $Rs.\, 40$ in the third month. If she continues to save in this manner,in how many months will she save $Rs.\, 2000$?

For an $A.P.$,the $5^{th}$ term is $30$ and the $12^{th}$ term is $100$. Find the sum of the first $20$ terms of the $A.P.$

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

For a given $A.P.$,the common difference is $5$ and its $15^{th}$ term is $72$. Find the first term of the $A.P.$ and its $50^{th}$ term.

The $10^{th}$ term of an $A.P.$ is $52$ and its $17^{th}$ term exceeds its $13^{th}$ term by $20$. Find the $A.P.$ and also its $30^{th}$ term.