Think First!

Consider the sequence $a_0,a_1,\ldots$ where $a_0=\frac{3}{11},$ $a_1 = -6,$ and $a_n= a_{n+1}+a_{n-1}$ for $n\ge 1.$ Find the value of: $a_{23}+a_{24}+a_{25}+a_{26}+a_{27}+a_{28}.$