Answer:
The answer is the option C
[tex]\frac{9}{3,125}, \frac{9}{15,625}[/tex]
Step-by-step explanation:
we have
[tex]9, \frac{9}{5},\frac{9}{25},\frac{9}{125},\frac{9}{625},...[/tex]
Rewrite the sequence
[tex]\frac{9}{5^{0}}, \frac{9}{5^{1}},\frac{9}{5^{2}},\frac{9}{5^{3}},\frac{9}{5^{4}},...[/tex]
therefore
The next two terms of the sequence are
[tex]\frac{9}{5^{5}}, \frac{9}{5^{6}},...[/tex]
[tex]\frac{9}{3,125}, \frac{9}{15,625},...[/tex]
Answer:
Option C.[tex]\frac{9}{3125} and \frac{9}{15625}[/tex]
Step-by-step explanation:
The given sequence is [tex]9, \frac{9}{5}, \frac{9}{5^{2} }, \frac{9}{5^{3}}, \frac{9}{5^{4}}.........[/tex]
This sequence is the geometric sequence of which first term is 9,
and common difference [tex]r=\frac{\frac{9}{5} }{9}=\frac{9}{(5)(9)}=\frac{1}{5}[/tex]
As we know explicit formula of a geometric sequence is
[tex]T_{n}=ar^{n-1}[/tex]
where n is the number of term.
We have to get 6th and 7th term of the sequence.
[tex]T_{6}=9.(\frac{1}{5})^{6-1}=\frac{9}{5^{5} }[/tex]
and [tex]T_{7}=9.(\frac{1}{5})^{7-1}=9.(\frac{1}{5})^{6}[/tex]
Therefore answer will be next two terms are [tex]\frac{9}{3125} and \frac{9}{15625}[/tex]
