$\displaystyle \displaystyle{\sum\limits^{10}_{r=1}\left(4r+\left (\frac{16}{5}\right)^r\right)=4\sum\limits^{10}_{r =1}r+\sum\limits^{10}_{r=1}\left(\frac{16}{5}\righ t)^r$ , and now the hints:
1) For any $\displaystyle \displaystyle{n\in\mathbb{N}\,,\,\,\sum\limits^n_{ k=1}k=\frac{n(n+1)}{2}}$ ;
2) for any $\displaystyle \displaystyle{1\neq a\in\mathbb{R}\,,\,n\in\mathbb{N}\,,\,\,\sum\limit s^n_{k=1}a^k=\frac{a^{n+1}-1}{a-1}}$
Now solve your problem (h)...
Tonio