Answer:
9. [tex]a_{8}[/tex] = [tex]\frac{1}{256}[/tex] or 0.00390625
10. [tex]a_{10}[/tex] = [tex]\frac{121}{1}[/tex] or 121
11. [tex]a_{100}[/tex] = [tex]\frac{100}{101}[/tex] or 0.99009
12. [tex]a_{5}[/tex] = [tex]-\frac{28}{5}[/tex] or 5.6
Step-by-step explanation:
9.
[tex]a_{8}[/tex] = [tex](\frac{1}{2}) ^{8}[/tex]
[tex]a_{8}[/tex] = [tex]\frac{1}{256}[/tex] or 0.00390625
10.
[tex]a_{10}[/tex] = [tex]\frac{(10+1)^{2}}{10-9}[/tex]
[tex]a_{10}[/tex] = [tex]\frac{11^{2}}{10-9}[/tex]
[tex]a_{10}[/tex] = [tex]\frac{121}{1}[/tex] or 121
11.
[tex]a_{100}[/tex] = [tex]\frac{100}{100+1}[/tex]
[tex]a_{100}[/tex] = [tex]\frac{100}{101}[/tex] or 0.99009
12.
[tex]a_{5}[/tex] = [tex]\frac{(-1)^{5+1} (5-1)(5+2)}{5}[/tex]
[tex]a_{5}[/tex] = [tex]\frac{(-1)^{6} (5-1)(5+2)}{5}[/tex]
[tex]a_{5}[/tex] = [tex]\frac {-1(4)(7)}{5}[/tex]
[tex]a_{5}[/tex] = [tex]\frac{-28}{5}[/tex]
[tex]a_{5}[/tex] = [tex]-\frac{28}{5}[/tex] or 5.6