Question

x/2+2x/2+3x/2+.....34x/2=35×17 Ajutor va rog

Answer 1

$\frac{x}{2} +\frac{2x}{2} +\frac{3x}{2} +...+\frac{34x}{2} = 35*17$

$x+2x+3x+...+34x= 2*35*17$

$x+2x+3x+...+34x \\ progresie \ aritmetica$

$r=a_2-a_1=2x-x=x$

$a_n=a_1+(n-1)r$

$34x=x+(n-1)x\\ 33x= nx-x\\ 34x=nx\\ n= \frac{34x}{x} =34$

$S_n=\frac{(a_1+a_n)*n}{2}$

$S_{34}= \frac{(x+34x)*34}{2}= 35x*17$

$35x*17 = 2*35*17$

$x=2$