G3.2 The sequence $\left\{a_{k}\right\}$ is defined as: $a_{1}=1, a_{2}=1$ and $a_{k}=a_{k-1}+a_{k-2}(k>2)$ If $a_{1}+a_{2}+\ldots+a_{10}=11 a_{b}$, find the value of $b$.
$\begin{array}{l}a_{1}=1, a_{2}=1, a_{3}=2, a_{4}=3, a_{5}=5, a_{6}=8, a_{7}=13, a_{8}=21, a_{9}=34, a_{10}=55 \\ a_{1}+a_{2}+\ldots+a_{10}=1+1+2+3+5+8+13+21+34+55=143=11 \times 13=11 a_{7} \\ b=7\end{array}$