Question

Efectuati: 5+8+11+...+305

Answer 1

$\displaystyle 5+8+11+...+305 \\ \\ 305=5+(n-1) \times 3 \\ \\ 305=5+3n-3 \\ \\ 3n=305-5+3 \\ \\ 3n=303 \\ \\ n= \frac{303}{3} \\ \\ n=101$

$\displaystyle S_{101}= \frac{10+100 \times 3}{2} \times 101 \\ \\ S_{101}= \frac{10 +300}{2} \times 101 \\ \\ S_{101}= \frac{310}{2} \times 101 \\ \\ S_{101}=155 \times 101 \\ \\ S_{101}=15655$