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Precalculus sequences and series worksheet12/13/2023 Students should realize that no, this is not an actual running time but acts as a placeholder so that on June 1st the equation amounts to 15 minutes. 5a answers may vary, see solutions 5b n 3 6a see solutions 6b 5 k 6c k 100 7 c, 8 e, 9 d, 10 e, 11 a. When using the a(0) term, ask students if there was ever a day Mallory ran 10 minutes. 3 The series in a, b, and c diverge, converge, and converge, respectively. I ask students when we want to start adding the five minutes, and they are able to reason that this is not until June 2nd, thus creating the need to “back track” our equation. Series are similar to sequences, except they add terms instead of listing them as separate elements. Thus, the first term corresponds to n 1, the second to n 2, and so on. Solution: Remember that we are assuming the index n starts at 1. Make sure students understand the necessity of the (n-1) when starting with June 1st. Practice Problem: Write the first five terms in the sequence. In the debrief, highlight the fact that there are two ways to write the explicit formula (and in fact, there are infinitely many, since we could use any day in June as our “anchor”). Be ready to build on student thinking and use the debrief to discuss both methods. Both of these strategies lead to the same sum formula, though written slightly differently. This sum of 175 will occur 15 times since there are 15 pairings of days. Another strategy is to realize that the days can be summed in any order and the sum of the first and last day is the same as the sum of the second and second to last day, is the same as the sum of the third and third to last day, and so on. Students use the idea of her average run time to find the sum of all 30 days. This idea of a constant (common) difference is critical to the rest of this lesson and ties in important ideas about a constant rate of change and linear functions. We specifically ask for June 29th so students recognize that her running time on that day is exactly five less than her running time on the 30th. While students may use a recursive pattern to find the first few values in the table, they should quickly recognize the need to make use of structure to find values for days later in June. Students identify that her time increases by five minutes every day and use this to fill in her running log. Interestingly, there are many strong connections between this section and Chapter 3, so the sequencing of course material actually works quite well. However, this is essential material in preparation for Calculus. That show us how many times we've added.Today students look at Mallory’s running times during the month of June to explore the idea of arithmetic sequences. Yes, at first glance this appears a random thing to throw in at the end of the course. In an arithmetic series, find the sum of the first 20 terms if the first term is -12 and the common difference is -5. We start out on the first item in the sequence, then work out how many times we have to add our constant to get to the final item. In an arithmetic sequence, axy1 32 and ax2 5. Find the nth term of the sequence, then find the 20th term. formal proofs Precalculus: Identities, logarithmic functions, exponential functions, trigonometric functions, series and sequences, probability. Determine whether or not the sequence is arithmetic. In order to de ne a sequence we must give enough information to nd its n-th term. Generate a sum formula for arithmetic sequences using the idea. E.g.: 1 2 3 4 ::: We represent a generic sequence as a1 a2 a3 :::,anditsn-th as a n. Write explicit rules to describe sequences with a common difference. This is what we do when we divide by the difference. Pre-Calculus Day 2 11.2 Homework Sequences & Series Worksheet Name 2015 Write the first five terms of the sequence. This extensive collection of series press sequence worksheets is recommended for large school undergraduate. An in nite sequence of real numbers is an ordered unending list of real numbers. More generally, for each hop you take, the number of hops is always one less than the number of squares you've been standing in. (a)the line passes through the point (1 3) with slope 13. 2.For each of the following conditions, nd the equation of the line that satis es those conditions. Worksheet 1: Precalculus review: functions and inverse functions 1.Find the domain and range of f (x) x+1 x2+x 2. You have to hop 4 times to get from your initial position in the first square to your final position in the fifth square. Worksheet 1: Precalculus review: functions and inverse functions. Then from the second to the third: 2 hops. You hop from the first to the second: 1 hop. Imagine there is a line of 5 squares on the ground. You have to add one because you're working out how many items there are in the series by counting how many hops it takes to get from the first to the last.
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