The $n^{th}$ term of the $A.P.$ $5, 10, 15, 20, \ldots$ is....... (in $n$)

The $n^{th}$ term of an $A.P.$ is given by $T_n = 5n - 2$. Then,the $12^{th}$ term of the $A.P.$ is:

Two distinct terms of an $A.P.$ cannot be........

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $5, 11, 17, 23, \ldots$

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?

For an $A.P.$,the $12^{th}$ term is $4$ and the $20^{th}$ term is $-20$. Find the $n^{th}$ term of the $A.P.$