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Find the sum of the first 16 terms in the sequence defined by the formula:

$$a_{n}=6048\left( \frac{1}{2}\right)^{n-1}$$

$\cfrac{12386115}{1024}$

$\cfrac{4128831}{1024}$

$\cfrac{6192963}{512}$

$12096$

None of the above