已知数列\(\{a_{n}\}\)，\(\{b_{n}\}\)的各项均为正数．在等差数列\(\{a_{n}\}\)中，\(a_{6}+a_{9}=a_{13}+3\)，\(a_{2}^{2}=a_{5}\)；在数列\(\{b_{n}\}\)中，\(b_{1}=1\)，\(3b_{n+1}^{2}+2b_{n}b_{n+1}-b_{n}^{2}=0.\)
\((Ⅰ)\)求数列\(\{a_{n}\}\)，\(\{b_{n}\}\)的通项公式；
\((Ⅱ)\)求数列\(\{a_{n}b_{n}\}\)的前\(n\)项和为\(T_{n}.\)