How do I expand this summation?

Question

So I just started doing these today and this has me stuck (It's a beginner question and i'm upset I'm stumped). So I have $\sum_{k=1}^{4}9k\sin(\frac{k\pi}{2})$ which I turn into $9\sum_{k=1}^{4}k\sin(\frac{k\pi}{2})$ annnnnnd that is as far as I got. How do I go about expanding this summation, thanks for all the help in advance.

Answer 1

HINT:

$$\sin\frac\pi2=1,\sin n\pi=0,\sin\left(\pi+\frac\pi2\right)=-\sin\frac\pi2$$

Answer 2

The sequence given by $$a_k = \sin\frac{\pi k}{2}$$ is periodic and fairly simple, you have $$ a_0=0,\quad a_1=1,\quad a_2=0, \quad a_3=-1,\quad a_4=0,\quad a_5=1,\quad\ldots$$ hence your sum just equals $9\cdot 1-9\cdot 3 = -18.$