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GUIDED NOTES – Lesson 8-3A Arithmetic Sequences & Series Name: ______________________ Period: ___ STANDARD: (F-BF.2) Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.OBJECTIVES: I can...Determine the common difference of a given sequence.Calculate a designated term in a sequence using a formula.Apply the formula for finding an arithmetic term to real-life problems.We now know that a sequence is an ordered list of numbers and that the sum of terms in a sequence is called a series.ARITHMETIC SEQUENCES are sequences that follow a pattern based on ____________. The number added to each term is a constant, fixed amount.The difference between one term and the next is called the ___________ ____________ ( ).This tells us how much more a term increases beyond the previous term.Examples:2, 6, 10, 14, … The common difference, d = _____15, 13, 11, 9, 7, … The common difference, d = _____5, ___, ___, ___, …The common difference, d = 312, ___, ___, …The common difference, d = 1.519, ___, ___, …The common difference, d = -3So far, we have done problems like this…Find the 8th term in the following sequence: an = 4, 6.5, 9, 11.5, 14,Easy right? We keep the sequence going and find that a8 = But what if you had to find the 33rd term? What if we needed to find the sum of those terms?It would require a lot of __________ and ___________, AND the chance of being off by a few numbers is very __________....…thus the need for the following formulas, which allow you to find any single term in an arithmetic sequence OR to find the sum of the designated terms in a sequence.ARITHMETIC TERM FORMULAARITHMETIC SUM FORMULAEXAMPLES: 1A) Find the 20th term of the sequence: an = 3, 7, 11, 15, ...1B) Find the sum of the first 20 terms above:2) Find the sum of the first 12 terms in this sequence:an = 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37,…3) Find the sum of the first 25 (S25) terms of this sequence, given that a25 = 145: an = 1, 7, 13, 19, …, 145APPLICATION Kyle started working for his brother, who owns a painting business. His brother didn’t think he would last on the job long, and told him he would pay him .50 cents for the first room he paints and increase his pay by .75 cents for each additional room he paints.How much will Kyle be making per room on the 20th room?How much money will he have grossed for those first 20 rooms? ................
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