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Chapter 11: Test Your Proficiency

Chapter 11: Test Your Proficiency. Directions: Select a section to work on. Work out each problem on a piece of paper. Click to check your answer. For detailed steps click on the provided link. Move on to the next problem or return to the menu. Sections. 11-1: The Arithmetic Sequence.

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Chapter 11: Test Your Proficiency

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  1. Chapter 11: Test Your Proficiency • Directions: • Select a section to work on. • Work out each problem on a piece of paper. • Click to check your answer. • For detailed steps click on the provided link. • Move on to the next problem or return to the menu. Sections 11-1: The Arithmetic Sequence 11-2: The Arithmetic Series 11-3: The Geometric Sequence 11-4: The Geometric Series I love sequences and series! 11-5: The Infinite Geometric Series 11-6: Recursion and Iteration 11-7: The Binomial Theorem 11-8: Mathematical Induction Applications/Word Problems

  2. Go on to the next problem 11-1: The Arithmetic Sequence Check Answer Return to Menu

  3. Go on to the next problem 11-1: The Arithmetic Sequence Click here if you would you like to see a detailed explanation. Return to Menu

  4. Go on to the next problem 11-1: The Arithmetic Sequence Step 1: Recall the formula to find a term of an arithmetic sequence. Step 2: Identify the known values and plug them into the formula. Step 3: Simplify and state the answer. Return to Menu

  5. Go on to the next problem 11-1: The Arithmetic Sequence Check Answer Return to Menu

  6. Go on to the next problem 11-1: The Arithmetic Sequence Click here if you would you like to see a detailed explanation. Return to Menu

  7. Go on to the next problem 11-1: The Arithmetic Sequence Step 1: Set up the problem and recall the formula to find a term of an arithmetic sequence. Step 2: Identify the known values and plug them into the formula. Step 3: Solve for d. Then find the missing arithmetic means by adding d to each preceding term. Return to Menu

  8. Go on to the next problem 11-1: The Arithmetic Sequence Check Answer Return to Menu

  9. Go on to the next problem 11-1: The Arithmetic Sequence Click here if you would you like to see a detailed explanation. Return to Menu

  10. Go on to the next problem 11-1: The Arithmetic Sequence Step 1: Recall the formula to find a term of an arithmetic sequence. Step 2: Identify the known values and plug them into the formula. Step 3: Solve for the missing value and state the answer. Return to Menu

  11. Go on to the next problem 11-1: The Arithmetic Sequence Check Answer Return to Menu

  12. Go on to the next problem 11-1: The Arithmetic Sequence Click here if you would you like to see a detailed explanation. Return to Menu

  13. Go on to the next problem 11-1: The Arithmetic Sequence Step 1: Recall the formula to find a term of an arithmetic sequence. Step 2: Identify the known values and plug them into the formula. Step 3: Solve for the missing value and state the answer. Return to Menu

  14. Go on to the next problem 11-1: The Arithmetic Sequence Check Answer Return to Menu

  15. Go on to the next problem 11-1: The Arithmetic Sequence Click here if you would you like to see a detailed explanation. Return to Menu

  16. Go on to the next problem 11-1: The Arithmetic Sequence Step 1: Recall the formula to find a term of an arithmetic sequence. Step 2: Identify the known values and plug them into the formula. Step 3: Simplify and state the answer. Return to Menu

  17. Go on to the next problem 11-2: The Arithmetic Series Check Answer Return to Menu

  18. Go on to the next problem 11-2: The Arithmetic Series The sum is -780. Click here if you would you like to see a detailed explanation. Return to Menu

  19. Go on to the next problem 11-2: The Arithmetic Series Step 1: Recall the formula to find the sum of an arithmetic series. Step 2: Identify the known values and unknown values. Step 3: Find the value of an. Step 4: Find Sn. Return to Menu

  20. Go on to the next problem 11-2: The Arithmetic Series Check Answer Return to Menu

  21. Go on to the next problem 11-2: The Arithmetic Series The sum is -4394. Click here if you would you like to see a detailed explanation. Return to Menu

  22. Go on to the next problem 11-2: The Arithmetic Series Step 1: Recall the formula to find the sum of an arithmetic series. Step 2: Identify the known values and unknown values. Step 3: Plug in the values to the formula and find Sn. Return to Menu

  23. Go on to the next problem 11-2: The Arithmetic Series Check Answer Return to Menu

  24. Go on to the next problem 11-2: The Arithmetic Series The sum is 285. Click here if you would you like to see a detailed explanation. Return to Menu

  25. Go on to the next problem 11-2: The Arithmetic Series Step 1: Recall the formula to find the sum of an arithmetic series. Step 2: Identify the known values and unknown values. Step 3: Find the value of n. Step 4: Find Sn. Return to Menu

  26. Go on to the next problem 11-2: The Arithmetic Series Check Answer Return to Menu

  27. Go on to the next problem 11-2: The Arithmetic Series The sum is 568. Click here if you would you like to see a detailed explanation. Return to Menu

  28. Go on to the next problem 11-2: The Arithmetic Series Step 1: Recall the formula to find the sum of an arithmetic series. Step 2: Find a1. Step 3: Find an. Step 4: Find the value of n. Return to Menu Click to see the rest of the explanation.

  29. Go on to the next problem 11-2: The Arithmetic Series Step 5: Plug in the values and find Sn. Return to Menu

  30. Go on to the next problem 11-3: The Geometric Sequence Check Answer Return to Menu

  31. Go on to the next problem 11-3: The Geometric Sequence Click here if you would you like to see a detailed explanation. Return to Menu

  32. Go on to the next problem 11-3: The Geometric Sequence Step 1: Recall the formula to find a term of a geometric sequence. Step 2: Plug in the given values. Step 3: Simplify. Note: Do not use rounded decimals unless the directions tell you to. Step 4: State the answer. Return to Menu

  33. Go on to the next problem 11-3: The Geometric Sequence Check Answer Return to Menu

  34. Go on to the next problem 11-3: The Geometric Sequence Click here if you would you like to see a detailed explanation. Return to Menu

  35. Go on to the next problem 11-3: The Geometric Sequence Step 1: Recall the formula to find a term of a geometric sequence. Step 2: Plug in the given values. Step 3: Simplify. Note: always enclose negative numbers in parentheses when raising to a power Step 4: State the answer. Return to Menu

  36. Go on to the next problem 11-3: The Geometric Sequence Check Answer Return to Menu

  37. Go on to the next problem 11-3: The Geometric Sequence Click here if you would you like to see a detailed explanation. Return to Menu

  38. Go on to the next problem 11-3: The Geometric Sequence Strategy: Use the definition of a geometric sequence: Each term after the first is found by multiplying the previous term by the common ration. Step 1: Find the value of r (the common ratio). Step 2: Find the next three terms in the sequence. Step 3: State the answer. Return to Menu

  39. Go on to the next problem 11-4: The Geometric Series Check Answer Return to Menu

  40. Go on to the next problem 11-4: The Geometric Series Click here if you would you like to see a detailed explanation. Return to Menu

  41. Go on to the next problem 11-4: The Geometric Series Strategy: Use the formula to find the sum of a geometric series with a finite number of terms, n. Step 1: Find the value of r (the common ratio), the value of a1, and the value of n. Step 3: State the answer. Step 2: Plug in r, a1 and n to the formula. Return to Menu

  42. Go on to the next problem 11-4: The Geometric Series Check Answer Return to Menu

  43. Go on to the next problem 11-4: The Geometric Series Click here if you would you like to see a detailed explanation. Return to Menu

  44. Go on to the next problem 11-4: The Geometric Series Strategy: Use the formula to find the sum of a geometric series with a finite number of terms, n. Step 2: Plug in r, a1 and n to the formula. Step 1: Identify the value of r (the common ratio), the value of a1, and the value of n from the sigma notation. Step 3: State the answer. Return to Menu

  45. Go on to the next problem 11-4: The Geometric Series Check Answer Return to Menu

  46. Go on to the next problem 11-4: The Geometric Series Click here if you would you like to see a detailed explanation. Return to Menu

  47. Go on to the next problem 11-4: The Geometric Series Strategy: Use the formula to find the sum of a geometric series with a finite number of terms, n. Step 2: State the answer. Step 1: Plug in r, a1 and n to the formula. Note: always enclose negative numbers in parentheses when raising to a power Return to Menu

  48. Go on to the next problem 11-5: The Infinite Geometric Series Check Answer Return to Menu

  49. Go on to the next problem 11-5: The Infinite Geometric Series The sum does not exist. Click here if you would you like to see a detailed explanation. Return to Menu

  50. Go on to the next problem 11-5: The Infinite Geometric Series Recall that an infinite geometric series only has a sum under certain conditions. The value of the common ratio, r, must be within the interval -1 < r < 1. Otherwise, the sum does not exist. Step 2: Compare the value of r to the interval -1 < r < 1. Step 1: Find the value of r. The value of r is outside of the interval. Step 3: Do not use the sum formula. Make the concluding statement. The sum does not exist. Return to Menu

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