Answer
88
Work Step by Step
The difference between two neighboring terms in the sum being
$a_{k+1}-a_{k}=\left(\frac{2}{3}(k+1)+4\right)-\left(\frac{2}{3} k+4\right)=\frac{2}{3}$
which does not depend on $\mathrm{k}$, and is constant, means that the sequence is arithmetic.
The sum of a finite arithmetic sequence is
$S_{n}=\frac{n}{2}\left(a_{1}+a_{n}\right)$
With $a_{1}=\frac{14}{3}, a_{11}=\frac{34}{3},$ we have
$S_{11}=\frac{11}{2}\left(\frac{14}{3}+\frac{34}{3}\right)=\frac{11}{2} \cdot \frac{48}{3}=88$
