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.

A. an = 273.75 ⋅ (1.04)n−1


B. an = 273.75 ⋅ (1.22)n−1


C. an = 225 ⋅ (0.22)n−1


D. an = 225 ⋅ (1.04)n−1

Answer 1

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

Explanation:

The nth term of geometric sequence is given by :-

`a_n=ar^(n-1)`

, 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

`a_6=(225)r^(5)` (2)

After the sixth month, she had $273.75 in her account.

i.e.
`a_6=273.75` (3)

From (2) and (3) , we have

`(225)r^(5)=273.75`

Divide both sides by 225 , we get

`r^5=1.21666666667=1.2167\\\\ r=(1.2167)^{(1)/(5)}\\\\ r=1.04000805172\approx1.04`

Substitute the value of a and r in (1) , we get

`a_n=225(1.04)^(n-1)`

Hence, the correct answer is D.
`a_n=225(1.04)^(n-1)`

Answer 2

D

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