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calculista

Answer:

The answer is the option C

\(\frac{9}{3,125}, \frac{9}{15,625}\)

Step-by-step explanation:

we have

\(9, \frac{9}{5},\frac{9}{25},\frac{9}{125},\frac{9}{625},...\)

Rewrite the sequence

\(\frac{9}{5^{0}}, \frac{9}{5^{1}},\frac{9}{5^{2}},\frac{9}{5^{3}},\frac{9}{5^{4}},...\)

therefore

The next two terms of the sequence are

\(\frac{9}{5^{5}}, \frac{9}{5^{6}},...\)

\(\frac{9}{3,125}, \frac{9}{15,625},...\)

Answer:

Option C.\(\frac{9}{3125} and \frac{9}{15625}\)

Step-by-step explanation:

The given sequence is \(9, \frac{9}{5}, \frac{9}{5^{2} }, \frac{9}{5^{3}}, \frac{9}{5^{4}}.........\)

This sequence is the geometric sequence of which first term is 9,

and common difference \(r=\frac{\frac{9}{5} }{9}=\frac{9}{(5)(9)}=\frac{1}{5}\)

As we know explicit formula of a geometric sequence is

\(T_{n}=ar^{n-1}\)

where n is the number of term.

We have to get 6th and 7th term of the sequence.

\(T_{6}=9.(\frac{1}{5})^{6-1}=\frac{9}{5^{5} }\)

and \(T_{7}=9.(\frac{1}{5})^{7-1}=9.(\frac{1}{5})^{6}\)

Therefore answer will be next two terms are \(\frac{9}{3125} and \frac{9}{15625}\)

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