The problem asks to find how much money Brad will have in his account after 6 months, given that he adds an equal amount of money each month.

Analyzing the problem:

1. Initial Amount (Month 0): $27.
2. Month 1: $44.
3. Month 3: $78.

Step 1: Find the monthly increment

To find how much Brad adds each month, calculate the difference between consecutive amounts:

• From $27 to $44: $44 - 27 = 17$
• From $44 to $78: $78 - 44 = 34$. This confirms he adds $17 each month.

Step 2: Write the pattern as an arithmetic sequence

The sequence can be expressed as: $a_n = 27 + 17n,$ where $n$ is the number of months and $a_n$ is the amount in the account.

Step 3: Calculate the amount after 6 months

Substitute $n = 6$ into the equation: $a_6 = 27 + 17 \times 6 = 27 + 102 = 129.$

Final Answer:

Brad will have $129 in his account after 6 months.

Would you like a detailed explanation of the arithmetic sequence or a graph of this pattern?

5 Related Questions:

1. What would Brad's total savings be after 12 months?
2. How can you write a general rule for savings with different initial amounts and monthly additions?
3. If Brad decides to double his monthly addition after 4 months, how would the sequence change?
4. How does this arithmetic sequence relate to linear equations in algebra?
5. What is the difference between arithmetic sequences and geometric sequences in patterns like this?

Tip: Look for consistent differences in sequences to identify patterns easily.