# Interpreting recursive equations to write a sequence to represent

## Recursive formula calculator

So this right over here is explicit. Recursive and explicit sequences Video transcript What I want to do in this video is familiarize ourselves with the notion of a sequence. So whatever k is, we started at 1. And I'm just going to add 3 for every successive term. And when you define a sequence recursively, you want to define what your first term is, with a sub 1 equaling 1. The example above gives the sequence of odd numbers 1, 3, 5, 7, So let's see what happens. The number you multiply or divide. If I wanted a more traditional function notation, I could have written a of k, where k is the term that I care about. It's going to be 7. We'd call it a sub 2. Now, in both of these cases, I defined it as an explicit function. And once again, you start at 3.

As an example, consider the table of values below. Well, they're saying, well, it's going to be a sub 2 minus 1. It may be the case with geometric sequences that the graph will increase or decrease.

And so a sub 1 is going to be 1. If k is equal to 2, you're going to have 1 plus 3, which is 4. Well, what about a sub 3?

## Interpreting recursive equations to write a sequence to represent

We could say that this right over here is the sequence a sub k for k is going from 1 to 4, is equal to this right over here. I could essentially do it defining our sequence as explicitly using kind of a function notation or something close to function notation. Well, I could say that this is equal to-- and people tend to use a. We would call that a sub 1. This just means we're going to keep going on and on and on. I think you get the picture-- a sub 3. So let's see. To find the nth square number, you first need to find the previous n - 1 square numbers. This right over here is a plus 3. But I want to make us comfortable with how we can denote sequences and also how we can define them. And then if you want the second term, it's going to be the first term plus 4. So it's going to be 1 plus 3, which is 4. But I'll do a again-- a sub k. To summarize the process of writing a recursive formula for a geometric sequence: 1.

Now, there's a bunch of different notations that seem fancy for denoting sequences. This just means we're going to keep going on and on and on. And you keep adding 4.

Well, I could say that this is equal to-- and people tend to use a. So the same exact sequence, I could define it as a sub k from k equals 1 to 4, with-- instead of explicitly writing the numbers here, I could say a sub k is equal to some function of k. So it's going to be 1 plus 3, which is 4.

Role in the Curriculum Informally, recursive functions are sometimes called Now-Next equations because they describe the next term in relation to the current, or now, term.

So we're adding 4 one less than the term that we're at.

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