Answer :
Answer:
D
Step-by-step explanation:
The geometric sequence formula is:
An=a*r^(n-1)
An= nth term of the sequence
a= first term of the sequence. In this case, the amount Monica had in the first month
r= common ratio. In this case, is the interest rate, which is constant in all months.
n= number of periods
Following this equation, option A and B are not correct because "a" the first term of the sequence is $225.
It is not option C because Monica will have her first $225 plus interest not only the interest she gained, then the common ratio should be a number greater than 1.
It is option D and let´s proved it:
A6= 225*(1.04)^(6-1)
A6=225* (1.21665)
A6=$273.746
A6=$273.75
Answer: D. [tex]a_n=225(1.04)^{n-1}[/tex]
Step-by-step explanation:
The nth term of geometric sequence is given by :-
[tex]a_n=ar^{n-1}[/tex]
, where a= First term.
r= common ratio.
Given : The first month, she had $225 in her account.
i.e. a= $225
Put n= 6 and a= $225 in (1), we get
[tex]a_6=(225)r^{5}[/tex] (2)
After the sixth month, she had $273.75 in her account.
i.e. [tex]a_6=273.75[/tex] (3)
From (2) and (3) , we have
[tex](225)r^{5}=273.75[/tex]
Divide both sides by 225 , we get
[tex]r^5=1.21666666667=1.2167\\\\ r=(1.2167)^{\frac{1}{5}}\\\\ r=1.04000805172\approx1.04[/tex]
Substitute the value of a and r in (1) , we get
[tex]a_n=225(1.04)^{n-1}[/tex]
Hence, the correct answer is D. [tex]a_n=225(1.04)^{n-1}[/tex]