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

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: $1, 4, 9, 16, \ldots $

Justify whether it is true to say that the following are the $n^{\text{th}}$ terms of an $AP.$
$(i)$ $2n-3$
$(ii)$ $3n^{2}+5$
$(iii)$ $1+n+n^{2}$

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

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

If $a_{n} = 3 - 4n$,show that $a_{1}, a_{2}, a_{3}, \ldots$ form an $AP$. Also,find $S_{20}$.