The $20^{th}$ term of the $A.P.$ $2, -2, -6, -10, \ldots$ is.......

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

The total number of two-digit positive multiples of $7$ is:

If $S_{n}$ denotes the sum of the first $n$ terms of an $AP$,prove that $S_{12} = 3(S_{8} - S_{4})$.

For the $A.P.$ $4, 8, 12, 16, \ldots$,$T_{40} - T_{30} = \ldots$

Four numbers in increasing order form an $A.P.$ The sum of those numbers is $32$ and the ratio of the product of extremes to the product of means is $7: 15$. Find those numbers.