How to Find Common Differences?

To find the common difference in an arithmetic sequence, simply subtract any term from the term that follows it.

Understanding Common Differences

A common difference is a constant value added to each term in an arithmetic sequence to get the next term. This constant difference is what defines an arithmetic sequence.

Method to Determine Common Difference

The easiest way to find the common difference is:

• Subtract the first term from the second term.
• Alternatively, subtract the second term from the third term.
• Continue this pattern for any two consecutive terms in the sequence.

Example

Let's consider the arithmetic sequence: 2, 10, 18, 26, ...

1. Subtract the first term (2) from the second term (10): 10 - 2 = 8
2. Subtract the second term (10) from the third term (18): 18 - 10 = 8
3. Subtract the third term (18) from the fourth term (26): 26 - 18 = 8

As you can see, the common difference is 8. This is because we are adding 8 to each term to obtain the next.

General Formula

We can express the common difference, often denoted by 'd', more formally as:

d = a_n+1 - a_n

Where:

• d is the common difference.
• a_n+1 is any term in the sequence.
• a_n is the term immediately preceding a_n+1

Importance of Finding the Common Difference

Knowing the common difference is crucial for:

• Predicting subsequent terms in a sequence.
• Deriving the general formula for an arithmetic sequence.
• Solving problems involving arithmetic progressions.