![]() ![]() But for the sake of this problem, we see that A is equal to four and B is equal to negative 1/5. And so we could say g of n is equal to g of n minus one, so the term right before that minus 1/5 if n is greater than one. Would use the second case, so then it would be g of four minus one, it would be g of three minus 1/5. To find the fourth term, if n is equal to four, I'm not gonna use this first case 'cause this has to be for n equals one, so if n equals four, I Trying to find the nth term, it's gonna be the n minus oneth term plus negative 1/5, so B is negative 1/5. So if you look at this way, you could see that if I'm You see that right over there and of course I could have written this like g of four is equal to g of four minus one minus 1/5. And so one way to think about it, if we were to go the other way, we could say, for example, that g of four is equal to g of three minus 1/5, minus 1/5. The same amount to every time, and I am, I'm subtracting 1/5, and so I am subtracting 1/5. Term to the second term, what have I done? Looks like I have subtracted 1/5, so minus 1/5, and then it's an arithmetic sequence so I should subtract or add Let's just think about what's happening with this arithmetic sequence. This means the n minus oneth term, plus B, will give you the nth term. ![]() It's saying it's going to beĮqual to the previous term, g of n minus one. And now let's think about the second line. So we could write this as g of n is equal to four if n is equal to one. If n is equal to one, if n is equal to one, the first term when n equals one is four. Well, the first one to figure out, A is actually pretty straightforward. And so I encourage you to pause this video and see if you could figure out what A and B are going to be. So they say the nth term is going to be equal to A if n is equal to one and it's going to beĮqual to g of n minus one plus B if n is greater than one. Missing parameters A and B in the following recursiveĭefinition of the sequence. So let's say the first term is four, second term is 3 4/5, third term is 3 3/5, fourth term is 3 2/5. For use in multiple classrooms, please purchase additional licenses.- g is a function that describes an arithmetic sequence. The recursive formula has a wide range of applications in statistics, biology, programming, finance, and more.This is also why knowing how to rewrite known sequences and functions as recursive formulas are important. This product is intended for personal use in one classroom only. Enjoy and I ☺thank you☺ for visiting my ☺Never Give Up On Math☺ store!!!įOLLOW ME FOR MORE MAZES ON THIS TOPIC & OTHER TOPICS ![]() Please don't forget to come back and rate this product when you have a chance. This maze could be used as: a way to check for understanding, a review, recap of the lesson, pair-share, cooperative learning, exit ticket, entrance ticket, homework, individual practice, when you have time left at the end of a period, beginning of the period (as a warm up or bell work), before a quiz on the topic, and more. If they are the same, a common ratio exists and the sequence is geometric. ✰ ✰ ✰Ī DIGITAL VERSION OF THIS ACTIVITY IS SOLD SEPARATELY AT MY STORE HERE How To Given a set of numbers, determine if they represent a geometric sequence. They complete it in class as a bell work. ✰ ✰ ✰ My students truly were ENGAGED answering this maze much better than the textbook problems. Specifically, you might find the formulas a n a + ( n 1) d (arithmetic) and a n a r n 1 (geometric). After seeing the preview, If you would like to modify the maze in any way, please don't hesitate to contact me via Q and A. If you look at other textbooks or online, you might find that their closed formulas for arithmetic and geometric sequences differ from ours. But if you are trying to find the 41th term, the explicit formula is easier. If you are trying to find the fourth or third term, you can use recursive form. ![]() Please, take a look at the preview before purchasing to make sure that this maze meets your expectations. Recursive formula is very tedious, but sometimes it works a little easier. Students would have to complete 12 of the 15 to reach the end. ❖ How to find the common ratio given the first four terms of a geometric sequence ❖ The Recursive Formula of a Geometric Sequence: a1 = a & An = a (sub n-1) * r There are three steps to writing the recursive formula for a geometric sequence, and they are very similar to the steps for an arithmetic sequence: Find and double-check the common ratio (the. ✐ This product is a good review of "Finding the Recursive Formula of a Geometric Sequence". ![]()
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