How to Find the Common Difference of an Arithmetic Sequence Given Two Terms?

To find the common difference of an arithmetic sequence when given two terms, follow these steps:

1. Determine the Order: Subtract the order (position) of the two given terms. This result represents the number of common differences between those terms, as stated in the reference video .
2. Calculate the Difference of the Terms: Subtract the values of the two given terms.
3. Divide: Divide the difference of the terms (from step 2) by the difference of their orders (from step 1). This result is the common difference of the arithmetic sequence.

Formula:

The formula to find the common difference (d) is:

d = (term₂ - term₁) / (order₂ - order₁)

Where:

• term₁ is the value of the first term.
• term₂ is the value of the second term.
• order₁ is the order (position) of the first term.
• order₂ is the order (position) of the second term.

Example:

Let's say you are given the 3rd term of an arithmetic sequence is 10, and the 7th term is 26.

• Step 1 (Order Difference): 7 - 3 = 4 (There are 4 common differences between the 3rd and 7th terms).
• Step 2 (Term Difference): 26 - 10 = 16.
• Step 3 (Common Difference): 16 / 4 = 4.

Therefore, the common difference of this arithmetic sequence is 4.

Summary Table:

Step	Description	Example
1. Order Difference	Subtract the positions of the terms.	7 - 3 = 4
2. Term Difference	Subtract the values of the terms.	26 - 10 = 16
3. Common Difference	Divide the term difference by the order difference.	16 / 4 = 4

Key Takeaways:

• The common difference is constant throughout an arithmetic sequence.
• This method works for any two terms in the sequence.
• Understanding the positions (order) of the terms is crucial for accurate calculation.