Sequences

A sequence is a list of numbers following a rule — a function whose inputs are the term numbers $1, 2, 3, \dots$. Two kinds dominate Algebra I:

• Arithmetic — a constant common difference $d$: you add $d$ each step. The $n$th term is $a_n = a_1 + (n - 1)d$.
• Geometric — a constant common ratio $r$: you multiply by $r$ each step. The $n$th term is $a_n = a_1 \cdot r^{\,n-1}$.

You'll also switch between a recursive rule (how to get the next term from the last one) and an explicit rule (the $n$th term directly). These are real, released Regents questions.