Question

Rezolvati ecuatia : (3x-1) + (3x-4) +(3x-7) +...+(3x-58) = 790

Answer 1

(3x-1) + (3x-4) +(3x-7) +...+(3x-58) = 790
n=58-1/3+1
n=57/3+1
n=19+1=20 ( termeni )
(3x-1) + (3x-4) +(3x-7) +...+(3x-58) = 790
3x+3x+3x+..........+3x-1-4-7-.......-58=790
20*3x-(1+4+7+..+58)=790
20*3x-20(58+1)/2=790
20*3x-10*59=790
60x-590=790
60x=1380
x=23

Answer 2

$(3x-1) + (3x-4) +(3x-7) +...+(3x-58) = 790\\ \\ \Big(3x-(3\cdot 0+1)\Big)+\Big(3x-(3\cdot 1+1)\Big)+\Big(3x-(3\cdot 2+1)\Big)+....\\ ...+\Big(3x-(3\cdot 19+1)\Big)=790 \\ \\ 3x+3x+\underset{de~ 20~ ori}{\underbrace{...}}+3x-(3\cdot 0+1)-(3\cdot 1+1)-(3\cdot 2+1)-...\\ \\...-(3\cdot 19+1)=790\\ \\ 20\times3x-(3\cdot 0+1+3\cdot 1+1+3\cdot 2+1+...+3\cdot 19+1) = 790\\ \\ 60x-\Big(3\cdot (0+1+2+...+19)+1+1+1+\underset{de~20~ori}{\underbrace{...}}+1\Big) = 790$
$60x - \Big(3\times \dfrac{19\times(19+1)}{2}+20\Big)=790 \\ \\ 60x-\Big(3\times \dfrac{19\times 20}{2}+20\Big) = 790\\ \\ 60x-\Big(3\times 19\times 10+20\Big) = 790 \\ \\ 60x-\Big(10\times (19\times 3+2)\Big) = 790 \\ \\ 60x -10\times 59 = 790 \\ \\ 60x-590 = 790 \\ \\ 60x = 790+590\\ \\ 60x = 1380\\ \\ x = 1380:60\\ \\ \boxed{x = 23}$