Question

Dau corontia:
Aflati termenul x
x+2x+3x+..+20x=2100

Answer 1

$S_{20}=\frac{(x+20x)20}{2}=210x$
210x=2100 => x=10
Rezolvarea este facuta prin formulele de la progresia aritmetica

Answer 2

$\displaystyle x+2x+3x+...+20x=2100 \\ \\ x(1+2+3+...+20)=2100 \\ \\ x \cdot \frac{20(20+1)}{2} =2100 \\ \\ x \cdot \frac{20 \cdot 21}{2} =2100 \\ \\ x \cdot \frac{420}{2} =2100 \\ \\ x \cdot 210=2100 \\ \\ 210x=2100 \\ \\ x= \frac{2100}{210} \\ \\ x= 10$