The sum of $1^3 + 2^3 + 3^3 + 4^3 + ..... + 15^3$ is:

The difference between the fourth term and the first term of a Geometric Progression is $52.$ If the sum of its first three terms is $26,$ then the sum of the first six terms of the progression is

Let $S_k = \frac{1 + 2 + 3 + .... + k}{k}$. If $S_1^2 + S_2^2 + ....... + S_{10}^2 = \frac{5}{12}A$,then $A$ is equal to

If the sum of two extreme numbers of an $A.P.$ with four terms is $8$ and the product of the remaining two middle terms is $15$, then the greatest number of the series will be:

The sum to $n$ terms of $(2n - 1) + 2(2n - 3) + 3(2n - 5) + .....$ is

If $4^{th}$ and $8^{th}$ terms of a $G.P.$ are $24$ and $384$ respectively,then find out the first term and common ratio.