This problem involves a series of deposits that follow an arithmetic sequence. Let's break down the steps to find the total amount deposited into the account up to and including Ruth's 6th birthday.

Step 1: Understanding the Sequence

Ricardo starts by depositing $500 for Ruth's 1st birthday. For each subsequent birthday, the amount deposited increases by $200 compared to the previous year.

The sequence of deposits looks like this:

• 1st birthday: $500
• 2nd birthday: $500 + $200 = $700
• 3rd birthday: $700 + $200 = $900
• 4th birthday: $900 + $200 = $1100
• 5th birthday: $1100 + $200 = $1300
• 6th birthday: $1300 + $200 = $1500

Step 2: Determine the Total Amount Deposited

To find the total amount deposited up to and including her 6th birthday, sum the amounts deposited each year.

$\text{Total Amount} = 500 + 700 + 900 + 1100 + 1300 + 1500$

Let's calculate the total:

$500 + 700 = 1200$ $1200 + 900 = 2100$ $2100 + 1100 = 3200$ $3200 + 1300 = 4500$ $4500 + 1500 = 6000$

Final Answer:

The total amount of money Ricardo will have deposited into the account for Ruth up to and including her 6th birthday is $6000.

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:

1. What if Ricardo increased the deposit by $300 each year instead of $200?
2. How much will Ricardo deposit in total by Ruth's 10th birthday if the same pattern continues?
3. What would the total be if the initial deposit was $1000 instead of $500?
4. Can you find a general formula for the total amount deposited up to Ruth's $n$th birthday?
5. How much would Ricardo need to deposit on Ruth's 7th birthday if the sequence continues?

Tip: When dealing with arithmetic sequences, summing the sequence can often be simplified using the formula for the sum of an arithmetic series.