设\(\left\{ a_{n}\right\}\)是首项为\(1\)的等比数列，数列\(\left\{ b_{n}\right\}\)满足\(b_{n}\text{=}\dfrac{na_{n}}{3}\text{.}\)已知\(a_{1}\text{,}3a_{2}\text{,}9a_{3}\)成等差数列．

\((1)\)求\(\left\{ a_{n}\right\}\)和\(\left\{ b_{n}\right\}\)的通项公式；

\((2)\)记\(S_{n}\)和\(T_{n}\)分别为\(\left\{ a_{n}\right\}\)和\(\left\{ b_{n}\right\}\)的前\(n\)项和．证明：\(T_{n}\text{ < }\dfrac{S_{n}}{2}.\)