Notice how the difference is not the same between the numbers, but there is a pattern that's going on here. All you have to do is first find the common ratio and then we can set up using this equation over here. And in fact, there's a lot of similarities between how we did this for arithmetic sequences. So let's go ahead and take a look at our example here because sometimes you may be asked to write recursive formulas for geometric sequences. So these tend to grow a much faster and arithmetic sequences. Whereas in geometric sequences, these tend to grow very fast because they're exponential, right, they're gowhereas this is only 369 12. So these types of sequences, the numbers grow a little bit slower. And what we're gonna see here also is that uh generally addition grows a little bit slower than multiplication. Whereas in geometric sequences, you multiply numbers to get with the next term. So clearly we can see here that the only difference between these two is the operation that's involved for arithmetic, you always add numbers to get to the next term. A and the new term is gonna be the previous term times R whatever that common ratio is. So and in fact the sort of general sort of a sort of a structure that you'll see for these recursive formulas for geometric sequences is they'll always look like this. That's really all there is to it, the way that you use these formulas to find the next terms is exactly the same. While in this geometric sequence, we're gonna take the previous term and instead we have to multiply by three. So in this situation, we just took the previous term and added three. Remember, recursive formulas are just formulas that tell you the next term based on the previous term. Now, we can use this common ratio to find additional terms by setting up a recursive formula. So little R in this case is equal to three kind of like how in this case little D was equal to three. And the letter we use for this is little R. Now this ratio over here is called the common ratio. So instead of adding three to each number to get the next one, you have to multiply by three to get the next number. So for example, from 3 to 9, you have to multiply by three, from 9 to 27 you also multiply by three from 27 to 81 you multiply by three. For example, the common difference in this situation of the sequence was three, a geometric sequence is a special type where the ratio between terms is always the same number. So remember that arithmetic sequences are special types where the difference between terms was always the same. So I wanna show you how to do that and the basic difference between these two types. And what we're gonna see is that there's a lot of similarities between how we use the information and the pattern across the numbers to set up a recursive formula for these types of sequences. What I'm gonna show you in this video is that this is a special type of sequence called a geometric sequence sequence. It's constantly getting bigger, but there's still actually a pattern going on with this sequence. Clearly, we can see that the difference between numbers is never the same. But let's take a look at this sequence over here. So we just finished talking a lot about arithmetic sequences like for example, 369 12, where the difference between each number is always the same number.
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