Question

encontre o valor de x tal que 3+10+17+...+x=49

Answer 1

Explicação passo-a-passo:

Sn=n.(a1+an)/2

49=n.(3+x)/2

40=(3n+n.x)

_____________

An=a1+(n-1).r

x=3+(n-1).7

x=3+7n-7

x= 7n-4

__________

40=(3n+n.x)

40=3n+n.(7n-4)

40=3n+7n²-4n

40=7n²-1n

7n²-1n-40=0

∆=(-1)²-4.(7).(-40)

∆=1+1120

∆=1121

n'=[ 1+√1121]/2.(7)

n'=[ 1+√1121]/14

n"=[ 1-√1121]/2.(7)

n"=[1-√1121]/14

______________

para n'= (1+√1121)/14

x=7n-4

x=7.(1+√1121]/14-4

x= (7+7√1121)/14-4

x= (1+√1121)/2 -4

para n'= (1-√1121)/14

x=7n-4

x=7.(1-√1121)/14-4

x= (7-7√1121)/14-4

x= (1-√1121)/14-4