Resposta :
[tex]P.G(-1,4,-16,...)[/tex]
[tex]a_{1}=-1[/tex]
[tex]a_{2}=4[/tex]
[tex]q = a_{2}/a_{1}=4(-1)=-4[/tex]
[tex]a_{n}=a_{1}*q^{(n-1)}[/tex]
[tex]a_{6}=a_{1}*q^{(6-1)}[/tex]
[tex]a_{6}=a_{1}*q^{5}[/tex]
[tex]a_{6}=(-1)*(-4)^{5}[/tex]
[tex]a_{6}=(-1)*(-1024)[/tex]
[tex]a_{6}=1024[/tex]
______________________________
[tex]P.G(-2,4,-8,...)[/tex]
[tex]a_{1}=-2[/tex]
[tex]a_{2}=4[/tex]
[tex]q=a_{2}/a_{1}=4(-2)=-2[/tex]
[tex]S_{n}=a_{1}(q^{n}-1)/(q-1)[/tex]
[tex]S_{6}=a_{1}(q^{6}-1)/(q-1)[/tex]
[tex]S_{6}=(-2)([-2]^{6}-1)/(-2-1)[/tex]
[tex]S_{6}=(-2)(64-1)/(-3)[/tex]
[tex]S_{6}=2(63)/3[/tex]
[tex]S_{6}=2(21)[/tex]
[tex]S_{6}=42[/tex]
[tex]a_{1}=-1[/tex]
[tex]a_{2}=4[/tex]
[tex]q = a_{2}/a_{1}=4(-1)=-4[/tex]
[tex]a_{n}=a_{1}*q^{(n-1)}[/tex]
[tex]a_{6}=a_{1}*q^{(6-1)}[/tex]
[tex]a_{6}=a_{1}*q^{5}[/tex]
[tex]a_{6}=(-1)*(-4)^{5}[/tex]
[tex]a_{6}=(-1)*(-1024)[/tex]
[tex]a_{6}=1024[/tex]
______________________________
[tex]P.G(-2,4,-8,...)[/tex]
[tex]a_{1}=-2[/tex]
[tex]a_{2}=4[/tex]
[tex]q=a_{2}/a_{1}=4(-2)=-2[/tex]
[tex]S_{n}=a_{1}(q^{n}-1)/(q-1)[/tex]
[tex]S_{6}=a_{1}(q^{6}-1)/(q-1)[/tex]
[tex]S_{6}=(-2)([-2]^{6}-1)/(-2-1)[/tex]
[tex]S_{6}=(-2)(64-1)/(-3)[/tex]
[tex]S_{6}=2(63)/3[/tex]
[tex]S_{6}=2(21)[/tex]
[tex]S_{6}=42[/tex]