1. 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 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

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 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?

4. 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”!

5. 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

6. 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

7. Exploration: Each diagram shows the number of line segments needed to connect a set of n points, no three of which lie in a straight line. n=1 n=2 n=3 n=4 Create a Sequence with at least six terms to show the relationship between the number of points and the number of line segments needed to connect every point to every other point.  # of Points 123456 # of Line Segments 0136

8. Exploration 2: Diagonals are formed on regular polygons starting with a three sided polygon or equilateral triangle. The number indicates the number of sides in the polygon. n=3 n=4 n=5 n=6 Determine the number of diagonals in a regular polygon with 2- sides. Then determine the equation for the number of diagonals in a regular polygon of n sides. # of sides 3456n # of Diagonals 0136

9. 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 = a = 3 so Use t 1 7 = 3(1) 2 + b (1) +c 7 = 3 (1) +b +c 7 = 3 + b + c 4 = b + c Use t 2 16 = 3(2) 2 + b (2) +c 16 = 3 (4) + 2b + c 16 = 12 + 2b + c 4 = 2b + c 4 = b + c 4 = 2b + c 0 = b SUBSTITUTE 4 = b + c 4 = 0 + c 4 = c

12. 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!