1) [tex]P.G(-240,-120,-60,...)[/tex]
[tex]a_{1}=-240[/tex]
[tex]a_{2}=-120[/tex]
[tex]q = a_{2}/a_{1}=-120/(-240)=1/2[/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}=(-240)*(1/2)^{5}[/tex]
[tex]a_{6}=(-240)*(1/32)[/tex]
[tex]a_{6}=-240/32[/tex]
[tex]a_{6}=-15/2[/tex]
2)
a)
[tex]q = a_{2} / a_{1}[/tex]
[tex]q = a_{3} / a_{2}[/tex]
[tex]q = q[/tex]
[tex]a_{2} / a_{1} = a_{3} / a_{2}[/tex]
[tex]a_{2}*a_{2}=a_{1}*a_{3}[/tex]
[tex](a_{2})^{2}=a_{1}*a_{3}[/tex]
[tex](a_{2})^{2}=\sqrt{2}*5\sqrt{2} [/tex]
[tex](a_{2})^{2}=5* \sqrt{2} * \sqrt{2} [/tex]
[tex](a_{2})^{2}=5*2[/tex]
[tex](a_{2})^{2}=10[/tex]
[tex]a_{2}= \sqrt{10} [/tex]
b)
[tex]a_{1}= \sqrt{2} [/tex]
[tex]a_{2}= \sqrt{10} [/tex]
[tex]q = a_{2}/a_{1}= \sqrt{10}/\sqrt{2}=\sqrt{10/2}= \sqrt{5} [/tex]
c)
[tex]a_{n}=a_{1}*q^{(n-1)}[/tex]
[tex]a_{7}=a_{1}*q^{(7-1)}[/tex]
[tex]a_{7}=a_{1}*q^{6}[/tex]
[tex]a_{7}=\sqrt{2}*(\sqrt{5})^{6}[/tex]
[tex]a_{7}=\sqrt{2}*5^{6/2}[/tex]
[tex]a_{7}=\sqrt{2}*5^{3}[/tex]
[tex]a_{7}=\sqrt{2}*125[/tex]
[tex]a_{7}=125\sqrt{2}[/tex]
