Solution
The recursive formular for geometric sequence:
Recursive formula for a geometric sequence is
[tex]a_n=a_{n-1}\times r[/tex]
where r is the common ratio
[tex]\frac{1}{2},\frac{3}{4},\frac{9}{8},\frac{27}{16}[/tex][tex]\begin{gathered} r=\frac{T_2}{T_1}=\frac{T_3}{T_2} \\ r=\frac{3}{4}\div\frac{1}{2}=\frac{3}{4}\times\frac{2}{1}=\frac{3}{2} \\ r=\frac{9}{8}\div\frac{3}{4}=\frac{9}{8}\times\frac{4}{3}=\frac{3}{2} \end{gathered}[/tex]
This is called recursive formula for geometric sequence.
Hence the recursive formula =
[tex]a_1=\frac{1}{2},a_n=a_{n-1}\text{.}(\frac{3}{2})\text{ for }n\ge2[/tex]
