Formula for arithmetic progression

Here are the formulas for an arithmetic progression:

The formula for the $n$-th term of an arithmetic progression is:

$$a_n = a_1 + (n-1)d$$

where:

• $a_n$ is the $n$-th term
• $a_1$ is the first term
• $n$ is the term number
• $d$ is the common difference

The formula for the sum of the first $n$ terms of an arithmetic progression is:

$$S_n = \frac{n}{2}(a_1 + a_n)$$

or, by substituting $a_n$:

$$S_n = \frac{n}{2}(2a_1 + (n-1)d)$$

where:

• $S_n$ is the sum of the first $n$ terms
• $a_1$ is the first term
• $a_n$ is the $n$-th term
• $n$ is the number of terms
• $d$ is the common difference