 So here's a quick introduction to a very interesting topic in mathematics called the geometric sequence. And this is any sequence, any set of numbers that has a particular form. And as you'll see in this particular set, I have a number, a number times r, whatever that is, a number times r squared times r cubed, and so on, up to some point. And we have a finite number of terms here, so we have a finite geometric sequence. And there's two important features about this sequence. First, so our very first value here, a, is what's called the initial term. And then the other thing to notice here is that every term of the sequence is the preceding term times r, so a times r gives you ar. ar times r gives you ar squared. ar squared times r gives you ar cubed, and so on, all the way up to this last term. And this value ar, where we're multiplying the preceding term to get the next term, is called the common ratio of the geometric sequence. For example, find the first five terms in the geometric sequence of the initial term five, and common ratio two. So here's where my starting term is five, the very first term of the sequence is five, and every term is going to be two times the preceding term. So there's my initial term, and every term is going to be two times the one before it. So my initial term times two gives me my next term, times two gives me my next term, times two gives me my next term, and so on. Likewise, I can have a geometric sequence with a common ratio that's actually a fraction. These are a variety of reasons that we'll discuss later, much more common. So I have my initial term one and common ratio one-third. So the initial term is one, and every term is going to be one-third times the preceding term. So my next term, one-third times one, my next term after that, one-third times one-third, and so on. And so those are my first three terms.