Calculating the Age of the Oldest Brother: A Simple Arithmetic Puzzle

The simple yet intriguing puzzle of seven brothers being born two years apart, with the youngest being seven years old, presents an opportunity to explore arithmetic progression and basic mathematical concepts. Let's delve into the problem and find the age of the oldest brother.

Understanding the Problem

Given that the youngest brother is seven years old and the brothers are born two years apart, we can determine the ages of the brothers using a straightforward arithmetic sequence. An arithmetic sequence is a sequence of numbers in which the difference between any two successive members is a constant. Here, the constant difference (d) is 2 years.

Calculating the Ages

To calculate the age of the brothers, we can use the formula for the nth term of an arithmetic sequence:
An a (n - 1)d

Where: - An is the nth term (age of the nth brother), - a is the first term (age of the youngest brother, which is 7), - d is the common difference (2), - n is the term number (from the youngest to the oldest).

Age Calculation

Let's calculate the ages step by step:

Youngest brother: 7 years old (n 1) Second youngest: 7 (2 * 1) 7 2 9 years old (n 2) Third youngest: 9 (2 * 1) 9 2 11 years old (n 3) Fourth youngest: 11 (2 * 1) 11 2 13 years old (n 4) Fifth youngest: 13 (2 * 1) 13 2 15 years old (n 5) Sixth youngest: 15 (2 * 1) 15 2 17 years old (n 6) Oldest brother: 17 (2 * 1) 17 2 19 years old (n 7)

Therefore, the age of the oldest brother is 19 years old.

Alternative Method Using Arithmetic Sequence Formula

We can solve the problem using the arithmetic sequence formula:

An a (n - 1)d

Where: - a 7 (the age of the youngest brother), - d 2 (the common difference), - n 7 (since there are 7 brothers).

Substituting the values, we get:

A7 7 (7 - 1) * 2 7 6 * 2 7 12 19

This confirms that the oldest brother is 19 years old.

Conclusion

The problem is a simple application of arithmetic sequences, where understanding the pattern and using the appropriate formula can help us determine the ages quickly and accurately. This type of puzzle not only tests one's ability to recognize patterns but also reinforces the fundamentals of arithmetic.

Key Takeaways: - Understanding the concept of arithmetic sequences. - Applying the formula An a (n - 1)d. - Practicing basic arithmetic operations for solving real-world problems.

By breaking down the problem into smaller steps, we can see how simple arithmetic can be used to solve seemingly complex puzzles. Whether you are an academic or a casual reader, this problem is a fun and educational tool for enhancing logical reasoning and mathematical skills.