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Gee, I wish I could use my TI – 83!

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For each of the following sequences, determine the common difference and the level at which it occurs. 1. -3, 0, 5, 12, 21 2. 1, -2, -9, -20, -35 3. 6, 10, 14, 18, 4. - 10, -27, -56, -97 3 5 7 9 2 2 2 d = 2 at Level D2 Quadratic -3 -7 -11 -15 -4 -4 -4 d = -4 at Level D2 Quadratic 4 4 4 d = 4 at Level D1 Arithmetic -17 -29 -41 -12 -12 d = -12 at Level D2 Quadratic

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Now use the function to generate the first four terms for each of these quadratic functions. Determine the common difference. What relation does it have with the coefficient of the a 2 term? Quadzilla XY 15 211 319 429 XY 1-5 2-19 3-41 4-71 XY 17 226 357 4100 XY 1-2 2-8 3-18 4-32 d is 2 at D2 a is 1 d is -8 at D2 a is -4 d is 12 at D2 a is 6 d is -4 at D2 a is -2 Is there a PATTERN here?

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In a Quadratic Sequence there is a special relationship between a & d!d! The Relationship between a & d in a Quadratic Sequence The difference “d” from Level D2 is twice the coefficient of the n 2 or x 2 term in the general formula. So to determine the formula or rule for the nth term of a certain quadratic sequence, we must first find the common difference and divide by 2 to find the coefficient “a”!“a”!

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The general formula for the nth term of a quadratic sequence is Let’s determine the first 5 terms

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To determine the common difference, we subtract backwards. The first five terms of this sequence are”

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Now You Try! Use “d” to determine “a” and then solve two equations! The sequence is 7, 16, 31, 52, 79 9 15 21 27 6 6 6 d 2 =

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The Formula for the n th term of a Quadratic Sequence is 1. To algebraically determine the formula or expression for the n th term of a Quadratic Sequence we need to know the formula. 2. We need to know the common difference in order to determine the coefficient “a”. 7, 16, 29, 46, 67 3. We need to use the information from two terms to set up two equations. 1 2 4. We need to solve the resulting System of Equations to determine “b” & “c” 5. We need to replace a, b, & c in the general formula. STEPS

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The Sequence 7, 16, 29, 46, 67 1 2 d = 4 so a = 2 3 Two terms to set up two equations. 4 Solve for b & c by solving the System of Equations. SUBTRACT SUBTITUTE to find the other variable. METHOD Now we have

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Page 13 # 40, 41, 42 16 # 5, 8, 9 Remember, Homework is not meant to be a burden. It is meant to help you to reinforce the lesson and it helps you to remember the steps and proves whether you understand!

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Lesson 11.2 Arithmetic Sequences. 3 7 11 15 The slope and the common difference.

Lesson 11.2 Arithmetic Sequences. 3 7 11 15 The slope and the common difference.

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