Answer:
[tex]\large\boxed{6.\ \bold{G}\ \dfrac{n^2}{3}}[/tex]
[tex]\large\boxed{7.\ \bold{C}\ 0.25n-0.75}[/tex]
Step-by-step explanation:
[tex]6.\\\\a(1)=\dfrac{1^2}{3}=\dfrac{1}{3}\\\\a(2)=\dfrac{2^2}{3}=\dfrac{4}{3}\\\\a(3)=\dfrac{3^2}{3}=\dfrac{9}{3}=3\\\\a(4)=\dfrac{4^2}{3}=\dfrac{16}{3}\\\\a(5)=\dfrac{5^2}{3}=\dfrac{25}{3}\\\\a(6)=\dfrac{6^2}{3}=\dfrac{36}{3}=12\\\vdots\\\\a(n)=\dfrac{n^2}{3}[/tex]
[tex]7.\\a(1)=-0.5\\\\a(2)=-0.5+0.25=-0.25\\\\a(3)=-0.25+0.25=0\\\\a(4)=0+0.25=0.25\\\\a(5)=0.25+0.25=0.5\\\vdots\\a(n)=a(n-1)+0.25\\\\\text{It's an arithmetic sequence with first term}\ a_1=-0.5\\ \text{and the common difference}\ d=0.25.\\\\a(n)=a(1)+(n-1)d\\\\\text{Substitute:}\\\\a(n)=-0.5+(n-1)(0.25)\\a(n)=-0.5+0.25n-0.25\\a(n)=-0.75+0.25n\\a(n)=0.25n-0.75[/tex]
