Finding Fourier Series Coefficients
The answer is right there in the question. You have expressed the signal as linear sum of scaled complex exponentials. 

Now the question is fourier series coefficients of a complex exponential$$e^{j100\pi t}$$

So you can see from the summation of x(t) that you have mentioned in the question that there is only one fourier series coefficient $a_1$ with a fundamental frequency $\omega_0$ because there is only one complex exponential in the input.The value of $\omega_0$ is $$ 100\pi$$. So $f_0$ = $(100\pi)/(2\pi)$ = 50

The value of $a_1$ is 1.

In other words you can express $$x(t)=(1).\ e^{(100 \pi)(1)t}$$ to see that  k=1 and $a_1$=1.