Question

Leigha has a piggy bank on her dresser and wants to save money for a concert. She starts by putting $22.50 in the piggy bank the first day. After that, she will save $.50 a day. How much money will she have after 200 days? (note, we use the arithmetic sequence formula below because on day 1 she puts in the $22.50 and saves the $.50 each day after) =1+ ሺ−1ሻ

Answer 1

To find out how much money Leigha will have after 200 days, we can use the arithmetic sequence formula:

\[a_n = a_1 + (n - 1) \cdot d\]

Where:
- \(a_n\) is the amount of money after \(n\) days.
- \(a_1\) is the initial amount Leigha puts in, which is $22.50.
- \(n\) is the number of days, which is 200 in this case.
- \(d\) is the daily saving amount, which is $0.50.

Let's plug these values into the formula:

\[a_{200} = 22.50 + (200 - 1) \cdot 0.50\]

\[a_{200} = 22.50 + 199 \cdot 0.50\]

Now, calculate the value:

\[a_{200} = 22.50 + 99.50\]

\[a_{200} = 122.00\]

So, Leigha will have $122.00 in her piggy bank after 200 days.

Answer 2

Leigha will have $122.00 after 200 days of saving $0.50 each day

Explanation:

To find out how much money Leigha will have after 200 days, we can use the arithmetic sequence formula.

First, let's find the common difference, which is the amount Leigha saves each day. In this case, she saves $0.50 per day.

Next, we can use the formula:

nth term = a + (n - 1)d

Where:

- nth term represents the term we want to find (in this case, the amount of money Leigha will have after 200 days)

- a represents the first term (which is $22.50)

- n represents the number of terms (which is 200)

- d represents the common difference (which is $0.50)

Now, let's plug in the values into the formula:

Amount of money after 200 days = 22.50 + (200 - 1) * 0.50

Simplifying this equation:

Amount of money after 200 days = 22.50 + 199 * 0.50

Amount of money after 200 days = 22.50 + 99.50

Amount of money after 200 days = 122.00

Therefore, Leigha will have $122.00 after 200 days of saving $0.50 each day.