2. Make a T-chart and find a pattern with the difference tests. 1 st level Difference Test. Linear equation with a slope of 2. What needs to be done to 2, 4, 6, 8 to get 1, 3, 5, 7? Alternating signs means we have (-1) n-1 power. 2 nd level Difference Test. Quadratic equation What needs to be done to 1, 4, 9, 16 to get 2, 5, 10, 17?

3. Do you see a pattern?

6. The k values are 1 bigger than the powers on the 2.

7. Notice that all the properties creates summations that all start at k = 1 and ends with n.

8. Find each sum. Property #2 and #6. n = Property #3.Property #8. Property #1.

9. Property #2, #3, and #4. n = Property #7, #6, and #1.

10. Not k = 1, Property #5 Property #2.Property #5. n =

11. 1 st level difference test. +4 d = 4 a 1 = 2 a 40 = 2 + 4(40 – 1) a 40 = 2 + 4(39) = 158 n = 40 Treat the terms like points, as we did in Sect. 9.1, ( 4, 20 ) and ( 13, 65 ). The difference, d, is the same as the slope. Find the slope between the 2 points. Find a 1, use ( 4, 20 ) and ( 1, a 1 ) with the slope formula.

12. This is a visual approach to solving this problem. Make consecutive blanks for each term. ____, ____ a1a1 Make an equation from 20 to 65 with the 9 d’s. Now subtract the d value backwards for the 1 st term.

13. 101 101 times how many groups? 101 ( 50 ) = 5050 Build the formula. Where did the numbers come from? These two formulas go hand in hand. na1a1 a 150 = ? +11 d = 11 a1a1 anan n = ? d = -50 Solve for n. Find these values.

14. *3 r = 3 a1a1 n = 10 ____, ____ Make an equation from 36 to 16 with the 2 r’s. With two r values gives us 2 equations.

15. Multiply both sides by a –r. This creates opposite terms. Add the equations together and cancel terms. Factor out the S.Factor out the a 1 Divide by (1 – r). a 1 = 5n = 10 r = 2

16. ? ( ½ ) oo will continue to get smaller until it is zero! Dividing by ( ½ ) is the same as multiplying by the reciprocal of 2.

17. Determine when a series diverge or converge. If a finite sum approaches a number L as, we say the infinite geometric series converges. A series diverges when the sum is. An infinite geometric series will always converge when. This gives us two formulas for geometric series. An infinite geometric series will always diverge when.

18. 2 nd STAT – OPS #5 is the sequence formula. seq(function,variable,starting value,ending value) Find the first 5 terms of 2 nd STAT – MATH #5 is the sum formula. Used for Series questions. sum(seq(function,variable,starting value,ending value)) Find