If the sum of the first $40$ terms of the series $3+4+8+9+13+14+18+19+\ldots$ is $(102)m$,then $m$ is equal to:

Let $a_1, a_2, a_3, \ldots$ be an $A$.$P$. If $a_7 = 3$,the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero,then $n! - 4 a_{n(n+2)}$ is equal to :

If $x$ is the arithmetic mean and $y, z$ are the two geometric means between two positive numbers,then $\frac{y^3 + z^3}{xyz} = \dots..$

An arithmetic progression is written in the following way. The sum of all the terms of the $10^{\text{th}}$ row is..........

Write the first five terms of the following sequence and obtain the corresponding series:
$a_{1} = a_{2} = 2, a_{n} = a_{n-1} - 1, n > 2$

If $\log_x y, \log_z x, \log_y z$ are in $G.P.$,$xyz = 64$,and $x^3, y^3, z^3$ are in $A.P.$,then