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
Working with matrices as transformations of the plane | Matrices | Precalculus | Khan Academy
In a previous video, I talked about how a two by two matrix can be used to define a transformation for the entire coordinate plane. What we’re going to do in this video is experiment with that a little bit and see if we can think about how to engineer two…
Calculating a P-value given a z statistic | AP Statistics | Khan Academy
Fay read an article that said 26% of Americans can speak more than one language. She was curious if this figure was higher in her city, so she tested her null hypothesis: that the proportion in her city is the same as all Americans’ - 26%. Her alternative…
Free Solo 360 | National Geographic
Anybody could conceivably die on any given day, and we’re all gonna die eventually. [Applause] So, Lange just makes it far more immediate. You accept the fact that if anything goes wrong, you’re going to die, and that’s that. [Music] I wasn’t the kind of…
Bill Gates: COVID-19 has Set Back Global Health for Years | National Geographic
[Music] Bill, it’s so nice to talk with you about this goalkeeper’s report. But I was really struck how different it was from the last time we talked about goalkeepers in 2018, and that was so much of a more positive report. You know, all of the indicato…
Making Backwoods Glue | Live Free or Die
Nutria are rodents that were first brought to America to be farmed for their thick fur. Now they’re hunted for their meat, but to find them, Thorn has to head downriver to the marshlands. Fortunately for me, I already have a boat; I’m just trying to make …
Obligations of citizenship | Citizenship | High school civics | Khan Academy
In this video, we’re going to learn about the obligations of U.S. citizenship. Obligations are actions that citizens are required to fulfill, or they’ll face punishment by law. Unlike the responsibilities of citizenship we talked about in the last video, …