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Monique deposited her money in the bank to collect interest. The first month, she had $225 in her account. After the sixth month, she had $273.75 in her account. Use sequence notation to represent the geometric function.

an = 273.75 ⋅ (1.04)n−1
an = 273.75 ⋅ (1.22)n−1
an = 225 ⋅ (0.22)n−1
an = 225 ⋅ (1.04)n−1

Respuesta :

wegnerkolmp2741o

Answer:

an = 225 (1.04) ^ (n-1)

Step-by-step explanation:

We start with the initial amount

a1 = 225

Then we know the amount in the account the 6th month

a6 = 273.75

The formula is

an = a1 r^(n-1)

273.75 = 225  (r) ^ 5

Divide each side by 225

273.75/225 = 225/225  (r) ^ 5

1.216666666 = r^5

Take the 5th root of each side

1.216666666 ^ 1/5 = r^5 ^ 1/5

1.04 = r

The formula becomes

an = 225 (1.04) ^ (n-1)

PunIntended

Answer:

D. [tex]a_n=225*(1.04)^{n-1}[/tex]

Step-by-step explanation:

Let's use the geometric sequence recursive formula: [tex]a_n=a_1r^{n-1}[/tex], where [tex]a_n[/tex] is the nth term, [tex]a_1[/tex] is the first term, and r is the common ratio.

We see that since in the first month, Monique had $225 already, then that means [tex]a_1=225[/tex]. We just need to find the common ratio. Let's use the information given about how much money she has in the sixth month. This means that [tex]a_6=273.75[/tex]. Plug this into the formula to find r:

[tex]a_n=a_1r^{n-1}[/tex]

[tex]a_6=a_1r^{6-1}[/tex]

[tex]273.75=225*r^5[/tex]

[tex]r^5=1.217[/tex]

r ≈ 1.04

Thus, our formula is: [tex]a_n=225*(1.04)^{n-1}[/tex], which is choice D.