Understanding the nth Term Rule in Math for 14-Year-Olds

The nth term rule in math is a formula that tells you the value of any term in a number sequence based on its position (n).

Think of a sequence as a list of numbers that follow a pattern, like:

2, 4, 6, 8, 10, ...

Here, the numbers are increasing by 2 each time. If you want to find the 5th term, you count 5 numbers and get 10. But what if you want the 100th term? Instead of counting, you use the nth term rule.

Step 1: Identify the pattern

Look at how the numbers are changing. In our example, they increase by 2 each time.

Step 2: Use the general formula for nth term

For many sequences, the nth term rule looks like this:

nth term = a × n + b

Where:

• a is how much the sequence increases each time (the difference between terms)
• b is the starting adjustment, related to the first term

Step 3: Find the formula for the example

In 2, 4, 6, 8, ... the difference a is 2.

Now, to find b, plug the first term (when n=1) into the formula:

Term 1 = 2 × 1 + b = 2 + b

But the first term is 2, so:

2 + b = 2 → b = 0

So, the nth term rule is:

nth term = 2n

Step 4: Use the nth term rule

If you want to find the 100th term:

100th term = 2 × 100 = 200

Summary

• The nth term rule helps you find any term in a sequence without listing all terms.
• It’s usually a formula like an + b, where you find a from the difference between terms and b by plugging in the first term.
• This formula saves time and helps you understand the pattern in numbers.