create a pattern with the rule n-4
The correct answer and explanation is:
Pattern Rule: n – 4
Let’s create a pattern using the rule n – 4, where n represents each term in a sequence starting from a given number.
Let’s begin with the number 50 (you can start from any number), and apply the rule repeatedly:
- First term: 50
- Second term: 50 – 4 = 46
- Third term: 46 – 4 = 42
- Fourth term: 42 – 4 = 38
- Fifth term: 38 – 4 = 34
- Sixth term: 34 – 4 = 30
Final Pattern:
50, 46, 42, 38, 34, 30, …
Explanation (300 words):
In mathematics, a pattern is a sequence of numbers that follow a specific rule. In this case, the rule is n – 4, which means each number in the pattern is 4 less than the one before it. This type of pattern is known as an arithmetic sequence, where the difference between any two consecutive terms is constant. That constant difference here is -4.
To generate the pattern, we start with an initial number, such as 50. Applying the rule repeatedly involves subtracting 4 from each term to get the next. So, from 50, subtracting 4 gives 46. From 46, subtracting 4 gives 42, and so on. Each step follows the same operation, ensuring consistency in the pattern.
The general formula for the n-th term of an arithmetic sequence is:
Tₙ = a + (n – 1) × d,
where:
- Tₙ is the n-th term,
- a is the first term (in this case, 50),
- d is the common difference (here, -4),
- n is the position in the sequence.
This allows you to find any term without having to list all the previous ones.
Patterns like this are useful in many areas such as programming, budgeting, and planning schedules. Recognizing and applying rules like n – 4 helps build logical thinking and problem-solving skills.