Find the sum of all $\displaystyle 11$ terms of an A.P. whose $\displaystyle 6^{\text {th }}$ term is 30.

$\displaystyle \begin{array}{l}n=11 a_{6}=30 a+5 d=30 \ldots(i) \text { Now } \begin{aligned} S_{11} & =\frac{11}{2}[2 a+(11-1) d] \\ & =\frac{11}{2}[2 a+10 d]=\frac{11}{\not 2} \times \not 2[a+5 d] \\ & =11 \times 30[\text { Using }(i)] \\ & =330\end{aligned}\end{array}$