Question

Calculați sumă de tip gauss
5+8+11+...305

Answer 1

$\displaystyle 5+8+11+...+305 \\ 305=5+(n-1) \times 3 \\ 305=5+3n-3 \\ 3n=305-5+3 \\ 3n=303 \\ n=303:3 \\ n=101 \\ S_{101}= \frac{10+100 \times 3}{2} \times 101 \\ \\ S_{101}= \frac{10+300}{2} \times 101 \\ \\ S_{101}= \frac{310}{2} \times 101 \\ \\ S_{101}=155 \times 101 \\ S_{101}=15655$