The sum to $50$ terms of the series $\frac{3}{1^2} + \frac{5}{1^2 + 2^2} + \frac{7}{1^2 + 2^2 + 3^2} + \dots$ is:

If a clock strikes the appropriate number of times at each hour,how many times will it strike in a day?

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

The number which should be added to the numbers $2, 14, 62$ so that the resulting numbers may be in $G.P.$ is

The first two terms of a geometric progression add up to $12.$ The sum of the third and the fourth terms is $48.$ If the terms of the geometric progression are alternately positive and negative,then the first term is

Let $a, b$ and $c$ be the $7^{th}, 11^{th}$ and $13^{th}$ terms respectively of a non-constant $A.P.$ If these are also the three consecutive terms of a $G.P.$,then $\frac{a}{c}$ is equal to