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: 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\(^5\) = (\(\frac{1}{3}\))(\(\frac{2}{5}\))\(^5\) = \(\frac{32}{729}\)
