Answer: Recursive formula of the given geometric sequence is [tex]a_{n}=a_{1}r^{n-1}[/tex].
Step-by-step explanation:
All geometric sequences have a first term a and common ratio r .
Now, in the given question
The first term is [tex]a=\frac{1}{2}[/tex]
The common ratio [tex]r=\frac{3}{2}[/tex]
Now, fifth term is [tex]a_{5}=a_{1}r^{5-1}=a_{1}r^{4}[/tex]
[tex]=\frac{1}{2}\times \left ( \frac{3}{2} \right )^{4}=\frac{1}{2}\times \frac{81}{16}=\frac{81}{32}[/tex]
Sixth term [tex]a_{6}=a_{1}r^{6-1}=a_{1}r^{5}[/tex]
[tex]=\frac{1}{2}\times \left ( \frac{3}{2} \right )^{5}=\frac{1}{2}\times \frac{243}{32}=\frac{243}{64}[/tex]
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nth term is [tex]a_{n}=a_{1}r^{n-1}[/tex].
