Sum of First 30 Terms of an AP

Let the AP have first term $a$ and common difference $d$. $S_{11} = S_{19} \implies \frac{11}{2}[2a + 10d] = \frac{19}{2}[2a + 18d]$ $22a + 110d = 38a + 342d \implies 16a + 232d = 0 \implies 2a + 29d = 0$ The sum of the first 30 terms is: $S_{30} = \frac{30}{2}[2a + 29d] = 15 \times (0) = 0$