To get the next term in an arithmetic sequence, find the constant difference between consecutive terms and add it to the last known term. This is based on the fundamental property of arithmetic sequences, which states that the difference between any two successive terms is always the same.
Understanding Arithmetic Sequences
An arithmetic sequence is a sequence of numbers such that the difference between any two consecutive members is a constant. This constant difference is called the "common difference."
Key Concepts:
- Terms: The individual numbers in the sequence.
- Common Difference (d): The constant value added to each term to get the next term.
- First Term (a1): The initial value of the sequence.
Finding the Next Term
Here's how to find the next term in an arithmetic sequence, incorporating the information from the provided reference:
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Identify the Common Difference (d): Subtract any term from its following term. For example, in the sequence 2, 4, 6, 8..., the common difference (d) is 4 - 2 = 2.
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Add the Common Difference to the Last Term: Once you know the common difference, add it to the last known term in the sequence to find the next term. Using the same example, the next term after 8 would be 8 + 2 = 10.
Example
Let's say we have the arithmetic sequence: 1, 5, 9, 13...
- The common difference (d) is 5 - 1 = 4.
- To find the next term after 13, we add the common difference: 13 + 4 = 17.
Therefore, the next term in the sequence is 17.
Summary
In short, finding the next term in an arithmetic sequence involves identifying the constant difference between terms and adding that difference to the last term of the sequence. As the Explanation in the references states, "Simply find the difference between each term, and add it to the last term to find the next term."
