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GUIDED NOTES – Lesson 8-4 Geometric 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 have learned that arithmetic sequences are sequences that follow a pattern based on _____________. The number added to each term is a constant, fixed amount.1, 3, 5, 7, 9, 11, 13, … d = ____Geometric sequences are built on the same concept, but their patterns are based on ______________. 1, 2, 4, 8, 16, 32, …r = ____The fixed amount multiplied from one term to the next is called the ___________ _________( ). Geometric sequences increase at a much ______________ rate than arithmetic sequence.To find the common ratio, we divide a term by its previous term (or as how much is it multiplying by to get to the next tem).2, 6, 18, 54, … Common ratio, r = _____2, -4, 8, -16, … Common ratio, r = _____20, 10, 5, ___, ___, …Common ratio, r = _____5, ___, ___, ___, …Common ratio, r = 420, ___, ___, ___, … Common ratio, r = 1.5GEOMETRIC TERM FORMULAGEOMETRIC SUM FORMULAEXAMPLES: 1) Find the 7th term of the sequence: 2, 6, 18, 54, …2) Find the 10th term of the sequence: 4, 6, 9, 13.5, …3) Find the sum of the first 7 terms of the sequence: 2, 6, 18,… 4) Find the sum of the first 8 terms of the sequence: 4, 6, 9, 13.5, … APPLICATION Jackson gets a 3% pay increase every year (r=____). He currently makes $32,000. 5) How much will he be making his 10th year?6) How much will he have grossed after working for ten years? ................
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