The difference between successive terms refers to the value obtained by subtracting one term in a sequence from the term that immediately follows it. This is especially relevant in arithmetic sequences.
Understanding the Common Difference
In an arithmetic sequence, the "difference between successive terms" is specifically called the common difference. This value remains constant throughout the entire sequence.
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Definition: The common difference is the constant value added to each term to get the next term in the sequence.
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Formula: The formula to find the common difference (d) in an arithmetic sequence is:
d = a(n) - a(n - 1)
Where:
- a(n) is the nth term in the sequence.
- a(n - 1) is the term preceding the nth term (i.e., the (n - 1)th term).
Example
Consider the arithmetic sequence: 2, 5, 8, 11, 14...
To find the common difference:
- Take any term (e.g., 5) and subtract the preceding term (e.g., 2).
- d = 5 - 2 = 3
- You can verify this with any other pair of successive terms: 8 - 5 = 3, 11 - 8 = 3, etc.
Therefore, the difference between successive terms (the common difference) in this sequence is 3.
Other Sequences
While the "difference between successive terms" is most commonly associated with arithmetic sequences and their common difference, any sequence of numbers has a difference between successive terms. However, unlike arithmetic sequences, this difference may not be constant.
