Question

sume gauss 14+18+22+...+122

Answer 1

$\displaystyle 14+18+22+...+122 \\ \\ 122=14+(n-1) \times 4 \\ \\ 122=14+4n-4 \\ \\ 4n=122-14+4 \\ \\ 4n=112 \\ \\ n= \frac{112}{4} \\ \\ n=28$

$\displaystyle S_{28}= \frac{28+27 \times 4}{2} \times 28 \\ \\ S_{28}= \frac{28+108}{2} \times 28 \\ \\ S_{28}= \frac{136}{2} \times 28 \\ \\ S_{28}=68 \times 28 \\ \\ S_{28}=1904$