[tex]\large\boxed{\begin{array}{l}\rm (5,10,15...50)\\\rm a_n=50\\\rm a_1=5\\\rm r=10-5=5\\\rm a_n=a_1+(n-1)\cdot r\longrightarrow n=\dfrac{a_n-a_1}{r}+1\\\\\rm n=\dfrac{50-5}{5}+1\\\\\rm n=\dfrac{45}{5}+1\\\\\rm n=5+1=6\\\rm S_6=\dfrac{\backslash\!\!\!6\cdot(50+5)}{\backslash\!\!\!2}\\\\\rm S_6= 3\cdot55\\\rm S_6=165\end{array}}[/tex]
