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

Worked example: using recursive formula for arithmetic sequence | High School Math | Khan Academy


2m read
·Nov 11, 2024

We are told b of 1 is equal to negative 7, and b of n is equal to b of n minus 1 plus 12. They’re asking us to find the fourth term in the sequence. So, what we have up here, which you could use a function definition, it's really defining the terms of a sequence.

Especially if you were to input whole numbers in here, it’s the index on your sequence. So what we really want to do is we want to figure out what is b of 4 going to be equal to. Well, if we just blindly apply this, we would say, all right, b of 4.

So b of n is equal to b of n minus 1 plus 12. So it's going to be b of 4 minus 1 plus 12. Well, 4 minus 1 is just 3. So it's going to be equal to b of 3 plus 12. All I did is said, okay, well, we're not trying to figure out or we're not immediately trying to figure out what b of 1 is; we're trying to figure out what b of 4 is. So n is equal to 4.

So b of 4 is going to be equal to b of 4 minus 1, or b of 3 plus 12. Well, to evaluate this, we have to figure out what b of 3 is. So let's write that down. That’s what's fun about a recursive definition; you have to keep recursing backwards.

So b of 3, well, if n is 3, that's going to be equal to b of now n minus 1 is 2, b of 2 plus 12. Well, we don't know what b of 2 is; let's keep going. So we need to figure out b of 2. If we use the same definition, b of 2 is going to be equal to b of 2 minus 1 plus 12.

So b of 2 minus 1, that’s b of 1 plus 12. But we don't know what b of 1 is, so let's figure that out. b of 1 is equal to, well, here we can finally use this top clause, so b of 1 is equal to negative 7.

So now we can go and fill everything back in. If b of 1 is equal to negative 7, then we know that this right over here is negative 7. Now we can figure out that b of 2 is equal to negative 7 plus 12, which is equal to 5.

Well, if b of 2 is equal to 5, well then this is equal to 5 right over here. Then now we know that b of 3 is equal to 5 plus 12, which is equal to 17. Well, if we know that b of 3 is equal to 17, then we're ready to calculate what b of 4 is going to be.

b of 4 is now b of 3, which we figured out was 17 plus 12, which is equal to 29. And we are done.

More Articles

View All
Aqueous solutions | Solutions, acids, and bases | High school chemistry | Khan Academy
What we have here are drawings of five different glass beakers, each holding different liquids or combinations of liquids and other things. Now, the first one here, I would just call that liquid water. That’s in this beaker. We’re going to assume everyth…
Building a Bathhouse in the Arctic | Life Below Zero
When I first started bringing my kids in the woods, I wasn’t sure how they’d take to it, and it seems like it’s in their blood. It makes me feel real proud. Let’s go check out the bath house; we got some work to do ahead of us. Part of having these hot s…
No Need To Worry About A Recession!
[Music] You’ve got inflation fears out there. That is one of just many worries weighing on the averages. But in times of high volatility, you got to start looking around. Where can investors go for opportunity? Let’s bring in Kevin O’Leary. Kevin, you ar…
How this 96-year-old Secretary grew a $9,000,000 Fortune
What’s up you guys? It’s Graham here. So, I want to share a really cool story written by Corey Kildonan of the New York Times. It’s a great example of what can happen when you live frugally and invest consistently while still working a very modest nine-to…
1920s urbanization and immigration | Period 7: 1890-1945 | AP US History | Khan Academy;
[Narrator] During the Gilded Age, the population of the United States had started to shift sharply towards living in urban rather than rural environments. In 1900, 1⁄3 of the American population lived in cities, drawn by the wide availability of factory j…
In high jump, your centre of mass goes under the bar
[Applause] I am about 1.75 m tall, but some of the world’s best high jumpers can clear more than half a meter above. [Applause] [Music] That this is Josh Lodge, an Australian high jumper. What’s your personal best high jump? 2 minutes 22? That’s pretty h…