<image>Given the sequence $$\{a_{n}\}$$ where each term is a positive number. Observe the flowchart. When $$k=1$$ and $$k=2$$, we have $$S= \dfrac {1}{3}$$ and $$S= \dfrac {2}{5}$$, respectively.
$$(1)$$ Find the general term formula for the sequence $$\{a_{n}\}$$;
$$(2)$$ Let $$b_{n}=3^{n}a_{n}$$. Find the sum of the first $$n$$ terms, $$T_{n}$$, of the sequence $$\{b_{n}\}$$.