The second and fourth terms of an exponential sequence (G.P) are \(\frac{2}{9}\) and \(\frac{8}{81}\) respectively. Find the sixth term of the sequence 

A.

\(\frac{81}{32}\)

B.

\(\frac{9}{8}\)

C.

\(\frac{1}{4}\)

D.

\(\frac{32}{729}\)

Correct answer is D

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

= \(\frac{32}{729}\)