In simple terms, the common difference is the constant value added or subtracted in an arithmetic sequence. An arithmetic sequence is a list of numbers where the difference between any two consecutive terms is always the same. Think of it like climbing stairs where each step is the same height!
To find the common difference ($d$), simply subtract any term from the term that follows it. Here's the formula:
$d = a_{n} - a_{n-1}$
Where:
Consider the arithmetic sequence: 2, 5, 8, 11, 14...
So, the common difference ($d$) is 3.
It's easy to mix up common difference with common ratio. Let's clear up the confusion!
| Feature | Common Difference | Common Ratio |
|---|---|---|
| Definition | ➕ The constant value added/subtracted in an arithmetic sequence. | ➗ The constant value multiplied/divided in a geometric sequence. |
| Sequence Type | ➕ Arithmetic Sequence (e.g., 2, 4, 6, 8...) | ➗ Geometric Sequence (e.g., 2, 4, 8, 16...) |
| Calculation | ➖ Subtract a term from its subsequent term. | ➗ Divide a term by its preceding term. |
| Formula | $d = a_{n} - a_{n-1}$ | $r = \frac{a_{n}}{a_{n-1}}$ |
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