Question

A)x+(x+1)+(x+2)+...+(x+11)=78 B)10+20+30+..+x0 (cu bara deasupra)=360 C)x+11+22+33+...+77=2x-187

Answer 1

x + ( x +1) + ... + ( x +11 ) = 12x + ( 1 +2+ .,. + 11) =12x + ( 1 +11) ·11 /2 
= 12x + 12 · 11 /2  =12x + 11 ·12 :2 = 12x + 11·6 =12x + 66 
12x + 66 = 78   ;  12x = 78 -66             ; 12x = 12          ;  x = 1 
b.   ( 10  + 10x ) · x / 2  =360 
x0 = 10x  
10 · ( 1 + x) · x = 360 · 2 
( 1 +x) · x = 36 · 2 
numere consecutive   x · ( x + 1) = 72 = 8 · 9 
daca  x = 8 
 c. 
          x + 11 · ( 1 + 2+ ..... + 7) =2x - 187 
x + 11 · ( 1 + 7) · 7 :2  =2x  - 187 
187  + 8 · 7 :2 = 2x - x 
187 + 28  =x 
x = 215