Introduction to Sequences: Finite and Infinite

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  • 0:01 Sequences
  • 0:49 Finite Sequences
  • 2:11 Infinite Sequences
  • 3:09 Why It's Important
  • 3:42 Sample Problem
  • 4:15 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, we will learn about the many patterns that are possible in sequences. See how some sequences stop after a while and how some sequences never stop.


What is a sequence? A sequence is a string of things in order. Because sequences have order, we can usually find a rule or pattern that fits. There is one famous sequence that we use almost every day of our lives. It is also one of the first things we learn. Can you think of what that is? Since we are talking math, think of numbers that are in order. Yes, it is our counting numbers. We begin by learning 1, 2, 3, and so on. We might learn to count to 10 first. But then we learn that these numbers actually continue forever. You could spend your entire life counting and never reach the end of the counting numbers.

Now let's talk about what kinds of sequences we can expect to see.

Finite Sequences

First, we have finite sequences, sequences that end. These sequences have a limited number of items in them. For example, our sequence of counting numbers up to 10 is a finite sequence because it ends at 10. We write our sequence with curly brackets and commas between the numbers like this: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. You can see that this sequence has order to it. It begins with a 1 and goes up by ones. Each number is the previous number plus 1.

We can also have a finite sequence made up of other things besides numbers. It can be an ordered sequence of letters, for example. Our alphabet is a finite sequence beginning with a and ending with z: {a, b, c, . . .x, y, z}. It has an order that we understand. We can also make a finite sequence out of names. For example, the name Sarah can be made into the sequence {s, a, r, a, h}, which contains all the letters in the name in order.

We can also create a sequence out of special groups of numbers. For example, we can have a finite sequence of the first four even numbers: {2, 4, 6, 8}. We can have a finite sequence such as {10, 8, 6, 4, 2, 0}, which is counting down by twos starting at 10.

The possibilities are endless. We can keep going and going.

Infinite Sequences

And this takes us to infinite sequences, which are sequences that keep on going and going. They have no end. For example, our counting numbers is an infinite sequence because it has no end. We can keep on counting forever. We write infinite sequences with the first few numbers to show the pattern and then with three periods in a row to show that it keeps going, like this: {1, 2, 3, 4...}.

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