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Determining the Function from a Quadratic Sequence Algebraically!

Determining the Function from a Quadratic Sequence Algebraically!. Gee, I wish I could use my TI – 83!. For each of the following sequences, determine the common difference and the level at which it occurs. 1. -3, 0, 5, 12, 21. d = 2 at Level D2  Quadratic.

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Determining the Function from a Quadratic Sequence Algebraically!

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  1. Determining the Function from a Quadratic Sequence Algebraically! Gee, I wish I could use my TI – 83!

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

  3. 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 a2 term? Quadzilla 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?

  4. The Relationship between a & d in a Quadratic Sequence In a Quadratic Sequence there is a special relationship between a &d! 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”!

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

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

  7. 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 d2 = 6 6 6

  8. STEPS 1. To algebraically determine the formula or expression for the nth term of a Quadratic Sequence we need to know the formula. The Formula for the nth term of a Quadratic Sequence is 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.

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

  10. 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! Page 13 # 40, 41, 42 16 # 5, 8, 9

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