[tex]\displaystyle a).1+3+5+...+99 \\ \\ 99=1+(n-1) \times 2 \\ \\ 99=1+2n-2 \\ \\ 2n=99-1+2 \\ \\ 2n=100 \\ \\ n= \frac{100}{2} \\ \\ n=50[/tex]
[tex]\displaystyle S_{50}= \frac{2+49 \times 2}{2} \times 50 \\ \\ S_{50}= \frac{2+98}{2} \times 50 \\ \\ S_{50}= \frac{100}{2} \times 50 \\ \\ S_{50}=50 \times 50 \\ \\ S_{50}=2500[/tex]
[tex]\displaystyle b).3+7+11+15+...+43 \\ \\ 43=3+(n-1) \times 4 \\ \\ 43=3+4n-4 \\ \\ 4n=43-3+4 \\ \\ 4n=44 \\ \\ n= \frac{44}{4} \\ \\ n=11[/tex]
[tex]\displaystyle S_1_1= \frac{6+10 \times 4}{2} \times 11 \\ \\ S_1_1= \frac{6+40}{2} \times 11 \\ \\ S_1_1= \frac{46}{2} \times 11 \\ \\ S_1_1=23 \times 11 \\ \\ S_1_1=253[/tex]
