Find the $10^{th}$ term of the $A.P.$ $\sqrt{2}, 3 \sqrt{2}, 5 \sqrt{2}, \ldots$ (in $\sqrt{2}$)

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

Which of the following form an $AP$? Justify your answer.
$(i)$ $11, 22, 33, \ldots$
$(ii)$ $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots$
$(iii)$ $2, 2^2, 2^3, 2^4, \ldots$
$(iv)$ $\sqrt{3}, \sqrt{12}, \sqrt{27}, \sqrt{48}, \ldots$

Which term of the $A.P.$ $53, 48, 43, \ldots$ is its first negative term? Find that term.

How many terms of the $A.P.$ $8, 15, 22, \ldots$ add up to $1490$?

The $n^{th}$ term of an $A.P.$ is given by $T_{n} = -4n + 15$. Find the $15^{th}$ term and the common difference of the $A.P.$