Extending geometric sequences

0:00- [Voiceover] So we're told that the first four terms of a geometric sequence are given. So they give us the first four terms. And they say what is the fifth term in the sequence. And like always pause the video and see if you can come up with the fifth term. Well what we have to remind ourselves is for a geometric sequence each successive term is the previous term multiplied by some number.

0:23And that number we call the common ratio. So let's think about it. To go from negative 1/32, that's the first term to 1/8, what do we have to multiply by? What do we have to multiply by? Let's see. We're going to multiply, it's going to be multiplied by a negative since we went from a negative to a positive.

0:39So we're going to multiply by negative and there's going to be a one over let's see to go from a 32 to an eight, actually it's not going to be a one over. It's going to be, this is four times as large as that. It's going to be negative four. Negative 1/32 times negative four is positive 1/8.

1:03Just to make that clear. Negative 1/32 times negative four that's the same thing as times negative four over one. It's going to be positive. Negative times a negative is a positive. Positive four over 32. Which is equal to 1/8. Now let's see if that holds up. So to go from 1/8 to negative 1/2 we once again would multiply by negative four.

1:31Negative four times 1/8 is negative 4/8, which is negative 1/2 and so then we multiply by negative four again. So, let me make it clear. We're multiplying by negative four each time. You multiply by negative four again, you get to positive two. Because negative four over negative two, you can do it that way, is positive two.

1:53And so to get the fifth term in the sequence, we would multiply by negative four again. And so two times negative four is negative eight. Negative four is the common ratio for this geometric sequence. But just to answer the question, What is the fifth term? It is going to be negative eight.