GATE Electronics and Communications (EC) 2021 Solved Paper

The exponential Fourier series representation of a continuous-time periodic signal x(t) is defined as:
$\mathit{x}\left(\mathit{t}\right)=\sum _{\mathit{k}=-\mathit{\infty }}^{\mathit{\infty }}{\mathit{a}}_{\mathit{k}}{\mathit{e}}^{\mathit{j}\mathit{k}{\mathit{\omega }}_0\mathit{t}}$
Where ω₀ is the fundamental angular frequency of x(t) and the coefficients of the series are a_k. The following information is given about x(t) and a_k.
I. x(t) is real and even having a fundamental period of 6
II. The average value of x(t) is 2
III. ${\mathit{a}}_{\mathit{k}}=\{\begin{array}{cc}\mathit{k}& 1\le \mathit{k}\le 3\\ 0& \mathit{k}>3\end{array}.$
The average power of the signal x(t) (rounded off to one decimal place) is _______.