Arithmetic Sequence Formula

Property Use the recursive formula $a n = a {n 1} + d$ to find the next term in a sequence, where $a 1$ is the first term, $d$ is the common difference, and $n$ is the term number.

Examples For a sequence with $a 1 = 2$ and $d=7$, the second term is $a 2 = 2 + 7 = 5$. Continuing that same sequence, the third term is found using the second term: $a 3 = 5 + 7 = 12$. And the fourth term uses the third: $a 4 = 12 + 7 = 19$. The sequence begins $ 2, 5, 12, 19, \dots$.

Explanation This is the 'one step at a time' formula! It tells you how to get the next term ($a n$) if you already know the term right before it ($a {n 1}$). Just take your current term and add the common difference, $d$. It’s like taking one more predictable step on a staircase, over and over again.