Question

If a5/a3=4/9 and a2=4/9 find the nth geometric sequence.?

Answer 1

\(\large\tt \begin{align} \color{black}{
\dfrac{a_5}{a_3}=\dfrac{4}{9} \\~\\
\dfrac{ar^4}{ar^2}=\dfrac{4}{9} \\~\\
r^2=\dfrac{4}{9} \\~\\
r=\sqrt{\dfrac{4}{9}} \\~\\
r=\dfrac{2}{3}\\~\\~\\
a_2=\dfrac{4}{9}\\~\\
ar=\dfrac{4}{9}\\~\\
a\times \dfrac{2}{3}=\dfrac{4}{9}\\~\\
a=\dfrac{4}{9}\times \dfrac{3}{2}\\~\\
a=\dfrac{2}{3}\\~\\~\\
\text{nth term}\\
=ar^{n-1}\\~\\
=\dfrac{2}{3}\left(\dfrac{2}{3}\right )^{n-1}\\~\\
}\end{align}\)