Question

What is the recursive formula of the geometric sequence? 1/2, 3/4, 9/8, 27/16,...

Answer 1

Answer: Recursive  formula of the given geometric sequence is $a_{n}=a_{1}r^{n-1}$.

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 $a=\frac{1}{2}$

The common ratio $r=\frac{3}{2}$

Now, fifth term is $a_{5}=a_{1}r^{5-1}=a_{1}r^{4}$

$=\frac{1}{2}\times \left ( \frac{3}{2} \right )^{4}=\frac{1}{2}\times \frac{81}{16}=\frac{81}{32}$

Sixth term $a_{6}=a_{1}r^{6-1}=a_{1}r^{5}$

$=\frac{1}{2}\times \left ( \frac{3}{2} \right )^{5}=\frac{1}{2}\times \frac{243}{32}=\frac{243}{64}$

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nth term is $a_{n}=a_{1}r^{n-1}$.