Let $$\widetilde x\left[ n \right]\, = \,1 + \cos \left[ {{{\pi n} \over 8}} \right]$$ be a periodic signal with period 16. Its DFS coefficients are defined by
$${a_k}$$ = $${1 \over {16}}\sum\limits_{n = 0}^{15} {\widetilde x} \left[ n \right]\exp \left( { - j{\pi \over 8}kn} \right)$$ for all k. The value of the coeffcients $${a_{31}}$$ is _____________________.

If x>y>1, which of the following must be true? $$$\begin{array}{l}\mathrm i.\;\ln\left(\mathrm x\right)>\ln\left(\mathrm y\right)\;\;\;\;\;\;\;\;\;\;\mathrm{ii}.\;\;\mathrm e^\mathrm x>\mathrm e^\mathrm y\\\mathrm{iii}.\;\mathrm y^\mathrm x>\mathrm x^\mathrm y\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\mathrm{iv}.\;\cos\left(\mathrm x\right)>\cos\left(\mathrm y\right)\end{array}$$$

Find the missing sequence in the letter series below:
A, CD, GHI, ? , UVWXY