Question

Find the missing number in the following table:
$\begin{array}{ccc}4& 4& 68\\ 5& 1& 126\\ 7& 5& ?\end{array}$

Answer 1

$\begin{array}{ccc}4& 4& 68\\ 5& 1& 126\\ 7& 5& x\end{array}$
$\frac{68-4}{4}=\frac{64}{4}=16=4^2$
$\frac{126-1}{5}=\frac{125}{5}=25=5^2$
Similarly, the next should be $6^2$
$\therefore \frac{x-5}{7}=6^2=36$
$\Rightarrow x-5={25}^2$
x = 252 + 5
= 257