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An arithmetic sequence is a list of numbers where the difference between consecutive terms is always the same. This constant difference is known as the 'common difference'. In our example, the sequence begins with 6 and each term increases by a fixed amount. Looking at the given sequence:

6, 10, 14, ...

we can observe that each term after the first is obtained by adding the common difference to the previous term. So, starting from 6, we add 4 to get 10, then add 4 again to get 14, and so on. An arithmetic sequence is, in essence, a pattern of numbers that grow or shrink at a steady rate, making it quite straightforward to predict future terms or even to trace back to previous terms.

The 'common difference' in an arithmetic sequence is the key to understanding how the sequence behaves. It's the engine that drives the pattern of numbers forward or backward. To find the common difference, you simply take any term and subtract the one before it. In other words:

Common Difference (d) = Term2 - Term1
In our case, taking 10 (the second term) and subtracting 6 (the first term), we get 4. This common difference is consistent for every term in the sequence. It tells us how much we add to (or subtract from) each term to get to the next one. Importantly, if the common difference is positive, the sequence will increase; if it is negative, the sequence will decrease.

Knowing how to use the sequence formula is like having a roadmap for finding any term in a sequence without having to write out all the previous ones. The nth term of an arithmetic sequence can be found using the formula:

\[a_n = a + (n-1) \times d\]

where \(a_n\) is the nth term we're looking for, \(a\) is the first term, \(n\) is the term's position in the sequence, and \(d\) is the common difference. With the numbers from our example, putting \(a = 6\) and \(d = 4\), we get:
\[a_n = 6 + (n-1) \times 4\].

This formula is powerful because it allows you to jump directly to any term without calculating all the ones in between. For instance, if you want the 100th term, there's no need to list out 99 terms first - plug 100 into the formula where \(n\) is, and you'll have your answer.