Given the following sequence of numbers:

\(27,\quad 41,\quad 69,\quad 125,\quad 237\quad ...\)

Considering the common ratio is 2, the \(n^{th}\) term can be expressed as \(a\times 2^n + b\).

Find \(\frac { \left| a-b \right| }{ a+b } \)

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