Correct Answer: Option D

Explanation

ar = \(\frac{2}{9}\) .....(i) 

ar\(^3\) = \(\frac{8}{81}\) ......(ii) 

\(\frac{ar3}{ar} = \frac{8}{81} \times \frac{9}{2}\) 

r\(^2 = \frac{4}{9}\) 

r = \(\sqrt{\frac{4}{9}}\) 

= \(\frac{2}{3}\) 

ar = \(\frac{2}{9}\) 

a(\(\frac{2}{3}\)) = \(\frac{2}{9}\)

a = (\(\frac{2}{3}\)) = \(\frac{2}{9}\)

a = \(\frac{2}{9} \times \frac{3}{2}\)

a = \(\frac{1}{3}\) 

T\(_r\) = ar\(^5\) = (\(\frac{1}{3}\))(\(\frac{2}{5}\))\(^5\) 

= \(\frac{32}{729}\) 

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