Question

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

Answer 1

D.
`a_n=225*(1.04)^(n-1)`

Explanation:

Let's use the geometric sequence recursive formula:
`a_n=a_1r^(n-1)`, where
`a_n` is the nth term,
`a_1` 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
`a_1=225`. 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
`a_6=273.75`. Plug this into the formula to find r:

`a_n=a_1r^(n-1)`

`a_6=a_1r^(6-1)`

`273.75=225*r^5`

`r^5=1.217`

r ≈ 1.04

Thus, our formula is:
`a_n=225*(1.04)^(n-1)`, which is choice D.

Answer 2

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

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)