Consider two G.Ps. 2,2^2, 2^3, … and 4,4^2, 4^3, … of 60 and n terms respectively. If the geometric mean of all the 60+ n terms is (2)^(225/8), then…

Consider two G.Ps. $\displaystyle 2,2^2, 2^3, \ldots$ and $\displaystyle 4,4^2, 4^3, \ldots$ of $\displaystyle 60$ and $\displaystyle n$ terms respectively. If the geometric mean of all the $\displaystyle 60+\mathrm{n}$ terms is $\displaystyle (2)^{\frac{225}{8}}$, then $\displaystyle \sum_{\mathrm{k}=1}^{\mathrm{n}} \mathrm{k}(\mathrm{n}-\mathrm{k})$ is equal to :