Question

Obter o valor de x,para que a sequência seja uma PG(5x+1,x+1,×-2)

Answer 1

PG(A1,A2,A3)                   A1=5x+1  A2=x+1  A3=x-2
PG(5x+1,x+1,x-2)
q=A2\A1=A3\A2
A2^2=A1xA3
(x+1)^2=(5x+1)(x-2)
x^2+2x+1=5x^2-10x+x-2
x^2+2x+1=5x^2-9x-2
x^2-5x^2+2x+9x+1+2=0
-4x^2+11x+3=0
a=-4  b=11 c=3

delta=b^2-4ac                             x=-b+-raiz de 169\2a
delta=11^2-4(-4)(3)                      x=-11+-13\2(-4)
delta=121+48                               x=-11+-13\-8
delta=169                               x`=-11+13\-8=2\-8=-1\4
                                               x``=-11-13\-8=-24\-8=3

substituindo teremos que 3 e a resposta pois:
5x+1=5(3)+1=16
x+1=3+1=4
x-2=3-2=1