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

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

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