What are infinite sequences?

An infinite sequence is like a never-ending list of things that follow a pattern.

Imagine you're counting up on your fingers, 1, 2, 3, 4... and you just keep going forever, even when you run out of fingers. That's what an infinite sequence feels like! It’s a list that never stops, and each number (or item) in the list follows some kind of rule.

Think about your favorite cookie jar. Every day, Mom bakes one more cookie and adds it to the jar. So on Day 1, there’s 1 cookie; on Day 2, there are 2 cookies; on Day 3, there are 3 cookies... and this keeps going forever. That growing list of cookies is an infinite sequence, it just keeps getting bigger and bigger, without ever stopping!

Another way to think about infinite sequences is like a story that has no end. Each sentence in the story follows a rule or pattern. You read one sentence after another, and you know there are always more sentences coming, it never ends.

So an infinite sequence is just a list that goes on forever, following some kind of pattern!