Question

AJUTOOOOOR!!!!!!Sa se rezolve ecuatiile:
a)1+7+13+...+x=280
b)(x+1)+(x+4)+(x+7)+...+(x+28)

Answer 1

1+7+13+...+x=280

x=6k+1

1+7+13+...+(6k+1)=280

7+13+...+(6k+1)=279

(6*1+1)+(6*2+1)+...+(6k+1)=279

(6*1+6*2+...+6*k)+(1+1+...de k ori...+1)=279

6(1+2+...+k)+k=279

6*k*(k+1)/2 +k=279

3k(k+1)+k=279

3k^2 +4k-279=0

3k^2-27k+31k-279=0

3k(k-9)+31(k-9)=0

(k-9)(3k+31)=0, k>=0, rezulta k-9=0, k=9, x=6*9+1=55

La punctul b)...unde-i ecuatia?! avem doar o suma...