What is the common difference in the sequence \{8,11,14,17,20, \ldots\}?
Answer (1)
Find the difference between consecutive terms.
Subtract the first term from the second term: 11 − 8 = 3 .
Verify the result by subtracting the second term from the third term: 14 − 11 = 3 .
The common difference is 3 .
Explanation
Understanding the Problem We are given the sequence 8 , 11 , 14 , 17 , 20 , … and we want to find the common difference.
Calculating the Common Difference To find the common difference, we can subtract any term from its subsequent term. Let's subtract the first term from the second term: 11 − 8 = 3 .
Verifying the Result We can verify this by subtracting the second term from the third term: 14 − 11 = 3 . Similarly, 17 − 14 = 3 and 20 − 17 = 3 .
Final Answer Therefore, the common difference in the sequence is 3.
Examples
Sequences are used in many real-life situations, such as calculating loan payments or predicting population growth. For example, if you deposit $100 into a bank account each month, and the account earns $5 in interest each month, the sequence of your account balance would be an arithmetic sequence. Understanding arithmetic sequences can help you predict your future account balance.
