[tex]\displaystyle 1+4+7+10+...+100 \\ 100=1+(n-1) \times 3 \\ 100=1+3n-3 \\ 3n=100-1+3 \\ 3n=102 \\ n=102:3 \\ n=34 \\ S_{34}= \frac{2 +33 \times 3}{2} \times 34 \\ \\ S_{34}= \frac{2+99}{2} \times 34 \\ \\ S_{34}= \frac{101}{2} \times 34 \\ \\ S_{34}=101 \times 17 \\ S_{34}=1717[/tex]
