Question

1+3+5+7+.......+73=
8+10+12..........+32=

Answer 1

$\displaystyle a).1+3+5+7+...+73 \\ 73=1+(n-1) \times 2 \\ 73=1+2n-2 \\ 2n=73-1+2 \\ 2n=74 \\ n=74:2 \\ n=37 \\ S_{37}= \frac{2+36 \times 2}{2} \times 37 \\ \\ S_{37}= \frac{2+72}{2} \times 37 \\ \\ S_{37}= \frac{74}{2} \times 37 \\ \\ S_{37}=37 \times 37 \\ S_{37}=1369$

$\displaystyle b).8+10+12+...+32 \\ 32=8+(n-1) \times 2 \\ 32=8+2n-2 \\ 2n=32-8+2 \\ 2n=26 \\ n=26:2 \\ n=13 \\ S_{13}= \frac{16+12 \times 2}{2}\times 13 \\ \\ S_{13}= \frac{16+24}{2} \times 13 \\ \\ S_{13}= \frac{40}{2} \times 13 \\ \\ S_{13}=20 \times 13 \\ S_{13}=260$