If \(2{a}_{n+2}=5{a}_{n+1}-3{a}_{n}\), where \(n=0,1,2,\ldots\). If \({a}_{0}=\)3 and \({a}_{1}=4\), then the value of \…

If \(2{a}_{n+2}=5{a}_{n+1}-3{a}_{n}\), where \(n=0,1,2,\ldots\). If \({a}_{0}=\)3 and \({a}_{1}=4\), then the value of \(\sum _{k=1}^{100}{a}_{k}\) is equal to (28 Jan, Shift I, Memory Based)