Information of x(t)
$ N = 4 $
$ a_5 = 10 $
x(t) is a real and even signal.
$ \frac{1}{4}\sum^{3}_{0} |x[n]|^2 = 200\, $
Finding x(t) by using given information
$ a_1 = a_5 = 10 $
$ x(t) is a even siganl, so a_-1 = 10 $
$ Using parseval's relation, $
$ \sum^{2}_{-1} |a_k|^2 = 200 $
$ |a_-1|^2 + |a_1|^2 + |a_0|^2 + |a_2|^2 = 200 $
Then $ a_0 = a_2 = 0. $
$ x[n] = \sum^{2}_{-1} a_k e^{j\frac{2\pi}{4}kn} $
