Answer:
The recursive formula that is used to represent the same geometric sequence as formula is:
[tex]a_1=2[/tex]
and [tex]a_n=a_{n-1}\cdot \dfrac{1}{2}[/tex]
Step-by-step explanation:
We are given a formula as:
[tex]a_n=2\cdot (\dfrac{1}{2})^{n-1}[/tex]
Now, the first term of it is given by:
[tex]a_1=2\times (\dfrac{1}{2})^{1-1}\\\\\\a_1=2\times (\dfrac{1}{2})^0\\\\\\a_1=2[/tex]
Also, [tex]a_2=2\cdot (\dfrac{1}{2})^{2-1}\\\\\\a_2=2\cdot (\dfrac{1}{2})\\\\\\a_2=a_1\cdot \dfrac{1}{2}[/tex]
and similarly we get:
[tex]a_3=2\cdot (\dfrac{1}{2})^{3-1}\\\\\\a_3=2\cdot \dfrac{1}{2}\cdot \dfrac{1}{2}\\\\\\a_3=a_2\cdot \dfrac{1}{2}[/tex]
Hence, option: C is the correct answer.
