Big Ideas Math [IM3]: 7.5 - Using Recursive Rules with Sequences (Lecture & Problem Set) скачать в хорошем качестве

Big Ideas Math [IM3]: 7.5 - Using Recursive Rules with Sequences (Lecture & Problem Set)

Not that you've asked for my opinion, but having come hot off recording an IM1 video with similar focus (recursively defined sequences), I noticed too many similarities in the early-on portion of this problem set. If you recall it from IM1, this won't be any bit of a struggle (until some word problems... more on that later). Recursive functions have strange looking formulas, but this is how we logically think of our sequences. When you say something like "add 3 each time," or "multiply by 5 each time," that is an example of recursion. You are iterating through your sequence by using the previous term to obtain the next term. Explicit rules, on the other hand, use the position of the term to calculate its value (when finding the 100th term, for example, you substitute 100 into your equation). The tricky part about these rules are their appearances. I can't use subscript notation in this description, so I'll write them using function notation. ARITHMETIC: f(n) = f(n - 1) + d GEOMETRIC: f(n) = r*f(n - 1) Where f(n) is the value of the nth term, and f(n - 1) is the value of the previous term. We also note what the first term is so we know where to begin our sequence. Recursive rules are also good for special sequences, such as the Fibonacci sequence. These are sequences that might use the two previous terms to obtain the next term (such as 1, 1, 2, 3, 5, 8, ... adding the two previous terms to get the next term). If I want to find the value of two terms before, I use f(n - 2), for example. We can convert forms (from explicit to recursive, and vice versa) as long as we know what information we need, which for the most part are the first term and the common difference/ratio. You'll find that this problem set is pretty whiz-bang up through #52, but then it slows to a crawl from #53-70. The back-end is all word problems, has problems with multiple parts, requires a lot of calculator and spreadsheet use (not to mention new calculator modes/features I've never used in the past), I use some self-exploration time on a few problems, and you'll find I'm mentally tapped out on some problems that I can't for the life of me subtract correctly! This is all unedited, so what you see is what you get. If you're here for the front-end, this will come as a breeze. Apologies if those last 18 questions aren't the content you came for, but I can say that I somehow got through it! I apologize for not staying zoomed in on my spreadsheets all the time, especially if you're watching on a phone screen. I need to remind myself that you're not necessarily watching on a 34.1" monitor. :p - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - PDF DOWNLOADS Textbook (7.5): https://smallpdf.com/file#s=341edccb-... - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - TIMESTAMPS (separated by section) (0:00:00) Introduction (0:01:20) Lecture overview (0:21:17) Problem #1-2 (0:22:45) Problem #3-10 (0:35:48) Problem #11-22 (0:46:11) Problem #23-26 (0:49:02) Problem #27-28 (0:51:25) Problem #29-38 (0:57:54) Problem #39-40 (0:59:30) Problem #41-48 (1:06:18) Problem #49-50 (1:08:04) Problem #51-52 (1:12:53) Problem #53-54 (1:21:13) Problem #55-56 (1:25:04) Problem #57-58 (1:41:55) Problem #57b (corrected) (1:43:25) Problem #59 (1:46:46) Problem #60 (1:53:02) Problem #61-62 (1:58:38) Problem #63 (2:00:16) Problem #64 (2:06:06) Problem #65 (2:09:41) Problem #66 (2:11:03) Problem #67 (2:16:50) Problem #68 (2:17:34) Problem #69-70 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - BIG IDEAS MATH (IM3) PLAYLIST    • Big Ideas Math [IM3]