Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the ratio .........

The sum of the first n terms of the series $${1^2} + {2.2^2} + {3^2} + {2.4^2} + {5^2} + {2.6^2} + .........$$ is
$$n\,\,{\left( {n + 1} \right)^2}/2,$$ when $$n$$ is even. When $$n$$ is odd, the sum is .............

The solution of the equation $$lo{g_7}$$ $$lo{g_5}$$ $$\left( {\sqrt {x + 5} + \sqrt x } \right) = 0$$ is .............

The sum of integers from 1 to 100 that are divisible by 2 or 5 is ............