Question

I need help on both of these

Answer 1

`\large\boxed{6.\ \bold{G}\ (n^2)/(3)}`

`\large\boxed{7.\ \bold{C}\ 0.25n-0.75}`

Explanation:

`6.\\\\a(1)=(1^2)/(3)=(1)/(3)\\\\a(2)=(2^2)/(3)=(4)/(3)\\\\a(3)=(3^2)/(3)=(9)/(3)=3\\\\a(4)=(4^2)/(3)=(16)/(3)\\\\a(5)=(5^2)/(3)=(25)/(3)\\\\a(6)=(6^2)/(3)=(36)/(3)=12\\\vdots\\\\a(n)=(n^2)/(3)`

`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`