yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Extending geometric sequences | Mathematics I | High School Math | Khan Academy


2m read
·Nov 11, 2024

So we're told that the first four terms of a geometric sequence are given. They give us the first four terms. 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, all we have to remind ourselves is for a geometric sequence, for a geometric sequence, each successive term is the previous term multiplied by some number, and 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. So we're going to multiply. We're going to multiply by negative, and then it's going to be a 1 over—let's see—to go from a 32 to an 8. Actually, it's not going to be a 1 over; it's going to be—this is 4 times as large as that. It's going to be negative 4.

Negative 1/32 times negative 4 is positive 1/8. Just to make that clear, negative 1/32 times negative 4. That's the same thing as times negative 4 over 1. It's going to be positive—negative times a negative is a positive—positive 4 over 32, which is equal to 1/8.

And let's see if that holds up. So to go from 1/8 to negative 1/2, we once again would multiply by negative 4. Negative 4 times 1/8 is negative 4/8, which is negative 1/2.

And so then we multiply by negative 4 again. So let me make it clear. We're multiplying by negative 4 each time. You multiply by negative 4 again, you get to positive 2. Because negative 4—negative negative 4 over negative 2—you can view it that way—is positive 2.

And so to get the fifth term in the sequence, we would multiply by negative 4 again. And so 2 times negative 4 is negative 8.

Negative 4 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 8.

More Articles

View All
End behavior of rational functions | Mathematics III | High School Math | Khan Academy
So we’re given this function ( f(x) ) and it equals this rational expression over here. We’re asked what does ( f(x) ) approach as ( x ) approaches negative infinity? So as ( x ) becomes more and more and more and more negative, what does ( f(x) ) approac…
Responding To CRINGE Investment Advice | BEST and WORST
What’s up you guys? It’s Graham here. So, I would like to think of myself as being social media savvy. You know, I got a YouTube channel. I got an Instagram account that I post on every now and then. I even have a Facebook group that I browse every single…
Why you procrastinate so often
I don’t know if you’ve ever noticed this, but it seems like sometimes in life the more you want something, the harder it is to get. This seems to be the case with starting a business or writing a book or any of these big life plans we always dream about. …
Lac operon
We’re now going to talk about one of the most famous operons, and this is the Lac operon. It is part of the E. coli genome and is involved in the metabolism of lactose. The “Lac” right over here is referring to lactose, and so you can imagine that it code…
What Are You?
Are you your body? Well, kind of, right? But is there a line where this stops being true? How much of yourself can you remove before you stop being you? And does the question even make sense? Your physical existence is cells, trillions of them, at least …
Virtual Mindfulness Retreat with Khan Academy and Headspace
And the intention for today’s hour is really just to relax, um, just to unwind. Not a lot of information coming at you, just embodied practices. And I know that a lot of you probably have commitments at home right now, maybe kids coming in. And so really …