Question

Calculati : 4+6+8+10+...+202

Answer 1

$\displaystyle 4+6+8+10+...+202 \\ 202=4+(n-1) \times2 \\ 202=4+2n-2 \\ 2n=202-4+2 \\ 2n=200 \\ n=200:2 \\ n=100 \\ S_{100}= \frac{8+99 \times 2}{2} \times 100 \\ \\ S_{100}= \frac{8+198}{2} \times 100 \\ \\ S_{100}= \frac{206}{2} \times 100 \\ \\ S_{100}=103 \times 100 \\ S_{100}=10300$