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

For the finite $A.P.$ $40, 35, 30, \ldots, -200,$ find the $10^{th}$ term from the end.

Find the sum of all the $11$ terms of an $AP$ whose middle most term is $30$.

Write the first three terms of the $APs$ when $a$ and $d$ are as given below:
$a = \sqrt{2}, d = \frac{1}{\sqrt{2}}$

For an $A.P.$,the sum of the $4^{th}$ term and the $8^{th}$ term is $24$,while the sum of the $6^{th}$ term and the $10^{th}$ term is $34$. Find the first term $a$ and the common difference $d$ of the $A.P.$

Two APs have the same common difference. The first term of one $AP$ is $2$ and that of the other is $7$. The difference between their $10^{\text{th}}$ terms is the same as the difference between their $21^{\text{st}}$ terms,which is the same as the difference between any two corresponding terms. Why?