In an $AP$ given $a=3, n=8, S_n=192,$ find $d$.

Are $3, 3+\sqrt{2}, 3+2\sqrt{2}, 3+3\sqrt{2}, \ldots$ in $AP$? If they form an $AP$,find the common difference $d$ and write the next three terms.

For what value of $n$,are the $n^{th}$ terms of two $APs: 63, 65, 67, \ldots$ and $3, 10, 17, \ldots$ equal?

Two $APs$ have the same common difference. The difference between their $100^{th}$ terms is $100$. What is the difference between their $1000^{th}$ terms?

Does the sequence $-2, 2, -2, 2, -2, \ldots$ form an $AP$? If it forms an $AP$,write the next two terms.

Find the number of terms in the following $AP$: $7, 13, 19, \ldots, 205$.