设\(\{a_{n}\}\)是等差数列，\(\{b_{n}\}\)是等比数列，公比大子\(0\)，且\(a_{1}=b_{1}=3\)，\(b_{2}=a_{3}\)，\(b_{3}=4a_{2}+3.\)
\((Ⅰ)\)求\(\{a_{n}\}\)和\(\{b_{n}\}\)的通项公式；
\((Ⅱ)\)设数列\(\{c_{n}\}\)满足\(c_{n}=\begin{cases}{1,n\text{为奇数}}\\ {b_{\frac{n}{2}},n\text{为偶数}}\end{cases}\)，求\(\sum\limits_{i=1}^{2n}a_{i}c_{i}.\)