Understanding the nth Term of an Arithmetic Sequence with Examples

In mathematics, an arithmetic sequence is a sequence of numbers such that the difference between any two successive members is constant. This constant difference is called the common difference, denoted as d.

The Formula for the nth Term

To understand how to find the nth term of an arithmetic sequence, let's break down the formula and apply it to a specific example.

The formula for the nth term of an arithmetic sequence is given by:

Tn T1 (n - 1)d

Example

Consider the arithmetic sequence: 2, 3, 4, 5, ...

Step 1: Identify the Common Difference

The common difference d is the difference between any two consecutive terms.

d 3 - 2 1

Step 2: Apply the Formula

Now, we can find the nth term using the formula.

Tn 2 (n - 1) * 1

Step 3: Simplify the Formula

Simplifying the formula, we get:

Tn 2 n - 1

Tn n 1

Examples of Applying the Formula

Let's apply the simplified formula to find specific terms in the sequence.

Finding the First Term

For n 1:

T1 1 1 2

Finding the Second Term

For n 2:

T2 2 1 3

Finding the Third Term

For n 3:

T3 3 1 4

Finding the Fourth Term

For n 4:

T4 4 1 5

These examples demonstrate that the nth term of this sequence can be found by adding 1 to the term number (n).

Conclusion

Understanding the formula and applying it to an arithmetic sequence is a fundamental skill in mathematics. By identifying the common difference and using the appropriate formula, you can easily find any term in the sequence.

For more information on arithmetic sequences and other mathematical concepts, continue exploring related topics and resources.