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Jeopardy

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  1. Jeopardy Choose a category. You will be given a question. You must give the correct answer. Click to begin.

  2. Choose a point value. Choose a point value. Click here for Final Jeopardy

  3. Sequences Arithmetic Sequences Geometric Sequences Mathematical Induction Finite Differences 10 Point 10 Point 10 Point 10 Point 10 Point 20 Points 20 Points 20 Points 20 Points 20 Points 30 Points 30 Points 30 Points 30 Points 30 Points 40 Points 40 Points 40 Points 40 Points 40 Points 50 Points 50 Points 50 Points 50 Points 50 Points

  4. Find the 5th term if • an = 2n2 – n!

  5. Find the 5th term if • an = 2n2 – n! • 2(25) – 5(4)(3)(2)(1) = • – 70

  6. Find the 5th term • of this sequence: • a1 = 2; a2 = 5; • an = an-1 +an-2

  7. Find the 5th term • of this sequence: • a1 = 2; a2 = 5; • an = an-1 +an-2 • a1 = 2, a2 = 5, a3 = 7, • a4 = 12, a5 = 19

  8. Evaluate:

  9. 1 + 2 + 4 + 2 + 9 + 2 + 16 + 2 + 25 + 2 = 65

  10. What is the difference between a sequence and a series?

  11. A sequence is an ordered list of numbers; a series is a sum.

  12. Find the first term without a calculator: an = n / (n – 1)!

  13. Find the first term: an = n/(n – 1)! a1= 1/0! = 1/1 = 1

  14. How do you identify an arithmetric sequence?

  15. The terms in an arithmetic sequence have a common difference.

  16. What is the formula for the explicit formula for an arithmetic sequence?

  17. an = a1 + (n – 1)d

  18. Find the 101st term: 1 + 3 + 5 + …

  19. 1 + 3 + 5 + … a101 = a1+(n – 1)(d) a101 = 1+100(2) = 201

  20. Write in sigma notation: 1 + 4 + 7 + …+ 31

  21. 1 + 4 + 7 + …+ 31 =

  22. Write the recursive formula if a5 = 6 and a10 = 16.

  23. Write the recursive formula if a5 = 6 and a10 = 16. a1 = –2; an = an – 1+ 2

  24. How do you know if a sequence is geometric?

  25. The terms of a geometric sequence have a common ratio.

  26. What is the recursive formula for a geometric sequence?

  27. What is the recursive formula for a geometric sequence? a1 = ___; an = ran – 1

  28. What kinds of infinite series have sums?

  29. Infinite geometric series with |r| < 1 have sums.

  30. Find the explicit formula: ½, –1, 2, – 4, …

  31. Find the explicit formula: ½, –1, 2, – 4, … an = ½ (–2) n – 1 or (–1) n – 1(2) n – 2

  32. Find the sum: .25 + .0025 + .000025 + …

  33. .25 + .0025 + .000025 + …= a1/(1 – r) = .25/(1 – .01) = .25/.99 = 25/99

  34. What is the first step in mathematical induction?

  35. Show that the equation is true for n = 1.

  36. What is the second step in mathematical induction?

  37. Assume that the equation is true for n = some natural number k.

  38. What is the third step in mathematical induction?

  39. Show that if the equation is true for n = k, then it is also true for n = k + 1.

  40. What does a mathematical induction proof allow you to do?

  41. Mathematical induction allows you to prove that an equation is true for all natural numbers.

  42. What would you add to the left hand side to show that this equation is true by mathematical induction? 1 + 4 + …+ k2 = k(k – 1 )/2

  43. 1 + 4 + …+ k2+ (k + 1) 2 = k(k – 1 )/2

  44. How do you know the degree of an equation based on finite differences?

  45. The degree of the equation is how many levels of differences you need for them to repeat.

  46. How do you find the leading coefficient?

  47. The leading coefficient is the value of the difference that repeats divided by the degree factorial.

  48. Find the first term of an equation for this sequence: 3, 6, 13, 24, 39, …

  49. 3, 6, 13, 24, 39, … 3 7 11 15 4 4 4 degree = 2, l.c. = 4/2! = 2 2x2

  50. Given this sequence, 3, 6, 13, 24, 39, …and y = 2x2, find its next term.