AI Tutor
When you hit play on a music playlist, track 11 plays first, track 22 second, and track 33 third. There is no track 2.52.5 or track Ο€\pi.
A list of ordered items like this is a sequence, and mathematically, it is secretly just a function in disguise.
How does a simple list of numbers connect to the functions you graph in algebra?

Sequences Are Functions

A function is a mathematical rule that assigns every valid input from a set called the domain to exactly one output in a set called the range.
A sequence is a function where the input represents the term's position nn, and the output is the value of the term itself, written as ana_n or f(n)f(n).
Because positions are counted in whole steps, the domain of a sequence is always a subset of the integersβ€”usually the positive integers {1,2,3,4,… }\{1, 2, 3, 4, \dots\} or non-negative integers {0,1,2,3,… }\{0, 1, 2, 3, \dots\}.
If a sequence is just a function, what happens when we try to draw its graph?

Continuous Lines vs. Discrete Dots

A standard linear equation like f(x)=2x+1f(x) = 2x + 1 has a domain of all real numbers, so its graph forms a solid, unbroken line.
A sequence defined by an=2n+1a_n = 2n + 1 only allows integer inputs, making its graph discreteβ€”a series of separate, unconnected points plotted at (1,3),(2,5),(3,7)(1, 3), (2, 5), (3, 7), and so on.