Question

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

Answer 1

$\displaystyle 4+6+8+10+...+202 \\ \\ 202=4+(n-1) \times 2 \\ \\ 202=4+2n-2 \\ \\ 2n=202-4+2 \\ \\ 2n=200 \\ \\ n= \frac{200}{2} \\ \\ n=100$

$\displaystyle S_{100}= \frac{8+99 \times 2}{2} \times 100 \\ \\S_{100}= \frac{8+198}{2} \times 100 \\ \\ S_{100}= \frac{206}{2} \times 100 \\ \\ S_{100}=103 \times 100 \\ \\ S_{100}=10300$