As N goes to infinity of a seven is equal toe out. So to find the limits of the recursive sequences, we're going to assume that's the limit. So we're also going to be finding the limit of recursive sequences, um, recursive sequence. Besides, just find the recursive sequence, it's finding the limit. It is very important to keep up with your indices and make them match the other thing we're going to do with recursive formulas. So this is how the Rikers in formula works. That's what matches our record in formula, which is equal to a set of three plus three because N is equal to three and a sub three with seven plus three gives us 10. So if we have a sub four that's going to be equal to a sub three plus one. We need it to match a seven plus one and has to be to so that we can get a sub three. So that's what we're plugging into the right hand side of the equation. ![]() So if we have a to the n plus one and we need ace of to and plus one and two to match these up, we have a one plus one, which means and is a whole toe one. Sometimes it could be three end plus two, and it could get a little complicated to figure out these indices. So let's dive a little bit deeper into the sub scripts and how important they are with the record in formula. Equal toe four Ace of three is equal to a set of two plus three, which is equal to four plus three equal to seven, and this continues. So if I need to list my terms in a sequence, I need a sea of one, which is equal to one, and I'm given that Ace of two, which is my second term is equal to a sub and plus three, which is a sub one plus three, which is equal toe one plus three. So here we have our initial term, and here we have what we're calling our Rikers in formula again. And let's also say that we have that A to the end plus one is equal to a seven plus three. This is the initial, um, terminar sequence that we're given. So let's say we're looking at we have Eighths of one is equal to one. So that's what we're gonna look at real quickly. So one of the best ways to see what I'm talking about is just with an example. ![]() It's going to be called a Rick Ergin formula, and this is what we're going to be given now instead of what we have been given. So you're given the initial terms or terms you also need to be given a recursive formula in this formula is going to be an A to the end, plus one formula. So you are given the initial term of the sequence and that is usually a someone you might be be given a sea of 1/8 of two. You're going to be given an initial value. So four a recursive sequence instead of given, be given an ace of them. So this is where a recursive sequence you're going to be given. So just by plugging and whatever end is right into our ace events, that's what we've been doing so far, but with a recursive sequence. So we've been able thio calculate H terminar sequence directly just plugging in in. What we have been working at so far is we've just been looking at a seven directly as the value of it.
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