Let \( 0 < z < y < x \) be three real numbers such that \( \frac{1}{x}, \frac{1}{y}, \frac{1}{z} \) are in an arithmetic progression and \( x, \sqrt{2}y, z \) are in a geometric progression. If \( xy + yz + zx = \frac{3}{\sqrt{2}} xyz \), then \( 3(x + y + z)^2 \) is equal to ____________.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: