Answer:
The correct option is D) [tex]a_n = 225(1.04)^{n - 1}[/tex]
Step-by-step explanation:
Consider the provided information.
In the first month, she had $225 in her account.
After the sixth month, she had $273.75 in her account.
The geometric sequence is given by: [tex]a_n = a(r)^{n - 1}[/tex]
In the first month, she had $225 in her account. After the sixth month, she had $273.75 in her account.
Substitute a=225, [tex]a_n=273.75[/tex] and n=6 in above formula.
[tex]273.75= 225(r)^{6-1}[/tex]
[tex]\frac{273.75}{225}=(r)^5}[/tex]
[tex]r\approx 1.04[/tex]
Hence, the value of r is 1.04
Therefore, the required sequence notation to represent the geometric function is [tex]a_n = 225(1.04)^{n - 1}[/tex]
Hence, the correct option is D) [tex]a_n = 225(1.04)^{n - 1}[/tex]
