An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference, typically denoted by $d$.
For an arithmetic sequence $u_1, u_2, u_3, ...$, where $u_n$ represents the $n$th term:
$$u_n = u_{n-1} + d$$
where $d$ is the common difference.
Consider the sequence: 3, 7, 11, 15, 19, ...
Here, $a_1 = 3$ and the common difference $d = 4$.
Terms can also be represented as $a_n$ instead of $u_n$. The two notations are interchangeable.
The general formula for the $n$th term of an arithmetic sequence is:
$$u_n = u_1 + (n-1)d$$
where $u_1$ is the first term, $n$ is the position of the term, and $d$ is the common difference.
This is because for every term, you're adding $d$ to the previous term. To get to the $n$th term from the first term, you perform $n - 1$ additions of $d$.
To find the common difference quickly, subtract any term from the subsequent term: $d = a_{n+1} - a_n$
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