Respuesta :

sqdancefan

Answer:

c. 10

Step-by-step explanation:

First of all, the sum can be simplified.

[tex]\sum\limits^6_{n=1} {(x-3n)}=\sum\limits^6_{n=1} {x}-3\sum\limits^6_{n=1} {n}\\\\=6x-3\cdot\dfrac{6\cdot 7}{2} =6x-63[/tex]

This result can be used in the equation ...

6x -63 = -3

6x = 60 . . . . . add 63

x = 10 . . . . . . . divide by 6

_____

Comment on the ∑n

The sum of numbers 1 to n is n(n+1)/2. We have used that fact here. For this problem, the sum is short enough you can simply add it up: 1+2+3+4+5+6 = 21.

[tex]\bf \displaystyle\sum\limits_{n=1}^{6}~(x-3n)=-3\implies \sum\limits_{n=1}^{6}~x-\sum\limits_{n=1}^{6}~3n=-3\implies \sum\limits_{n=1}^{6}~x-3\sum\limits_{n=1}^{6}~n=-3 \\\\\\ 6(x)~~-~~3\left[ \cfrac{6(6+1)}{2} \right]=-3\implies 6x~~-~~3[3(7)]=-3\implies 6x - 63 = -3 \\\\\\ 6x=60\implies x=\cfrac{60}{6}\implies x=10[/tex]

Otras preguntas