[tex]\displaystyle 3+5+7+...+151 \\ \\ 151=3+(n-1) \times 2 \\ \\ 151=3+2n-2 \\ \\ 2n=151-3+2 \\ \\ 2n=150 \\ \\ n= \frac{150}{2} \\ \\ n=75[/tex]
[tex]\displaystyle S_{75}= \frac{6+74 \times 2}{2} \times 75 \\ \\ S_{75}= \frac{6+148}{2} \times 75 \\ \\ S_{75}= \frac{154}{2} \times 75 \\ \\ S_{75}=77 \times 75 \\ \\ S_{75}=5775[/tex]