Question

Suma mai multor nr intregi consecutive este -25. Numerele negative sunt mai multe decat cele nenegative. Cate nr sunt?

AJUTOR!!!#

Answer 1

-n.......-m......,-2,-1,0,1,2,3,........m        (m < n)   n - m = k       m = n - k =-(-n+k)
S1 = -m + ......0 +........+m = 0
 S = -n + (-n+1) + (- n+2) +.....+ (-n+k) = - 25
-n·(k+1) + (1+2+3+.....+k) = - 25
-n(k+1) + k(k+1)/2 =- 25
-(k+1)(n - k/2) = - 25      (k+1)(n - k/2) = 25
25 = 5·5 ⇒    k +1 = 5    k = 4
n - k/2 = 5    n = 5+ 2     n = 7      m =3
-7 - 6 - 5 -4 - 3 = - 25
numerele sunt: -7,-6,-5,-4,-3,-2,-1,0,1,2,3 ⇒     3- (-7) +1 = 11 numere