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In Exercises 1 to 10, use inductive reasoning to predict the next number in each list. 1. 4, 8, 12, 16, 20, 24,? 2. 5, 11, 17, 23, 29, 35,? 3. 3, 5, 9, 15, 23, 33,? 4. 1, 8, 27, 64, 125,? 5. 1, 4, 9, 16, 25, 36, 49,? 6. 80, 70, 61, 53, 46, 40,? 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 ,? 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 ,? 9. 2, 7, -3, 2, -8, -3, -13, -8, -18,? 10. 1, 5, 12, 22, 35,?
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In Exercises 1 to 10, use inductive reasoning to predict the next number in each list. 1.4, 8, 12, 16, 20, 24, __5 _1_ _ 2. 5, 11, 17, 23, 29, 35, _-,_ __1 _. 3. 3, 5, 9, 15, 23, 33, _, _. _, _,_ 4. 1, 8, 27, 64, 125, __,_ __ 5. 1, 4, 9, 16, 25, 36, 49, _,_ _ __ 6. 80, 70, 61, 53, 46, 40,_ _, _,_ -,_ 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 , _, __1 __. 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 , _,_ , _,_ -,_ 9. 2, 7, -3, 2, -8, -3, -13, -8, -18,_ __ _,_ 10. 1, 5, 12, 22, 35, _-1_ _ __
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Use inductive reasoning to predict the most probable next number in each list. 1. 1, 8, 27, 64, 125, ? 2. 80, 70, 61, 53, 46, 40, ? 3. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 , ? 4. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 , ? 5. 2, 7, -3, 2, -8, -3, -13, -8, -18, ?
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In Exercises 1 to 10, use inductive reasoning to predict the 6, 80, 70, 61, 53, 46,40, ? next number in each list. 1. 4, 8, 12. 16, 20, 24. ? 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 , ? 2. 5, 11, 17,23, 29, 35, ? 3. 3. 5.9.15.23.33.? 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 , ? 4. 1, 8. 27. 64. 125.? 9. 2.7.-3.2.-8.-3.-13.-8.-18.? 5. 1, 4, 9, 16, 25. 36, 49, ? 10. I. 5. 12. 22. 35. ?
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In Exercises 1 to 10, use inductive reasoning to predict the next number in each list. 1.4, 8, 12, 16, 20, 24, __5 _1_ _ 2. 5, 11, 17, 23, 29, 35, _-,_ __1 _. 3. 3, 5, 9, 15, 23, 33, _, _. _, _,_ 4. 1, 8, 27, 64, 125, __,_ __ 5. 1, 4, 9, 16, 25, 36, 49, _,_ _ __ 6. 80, 70, 61, 53, 46, 40,_ _, _,_ -,_ 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 , _, __1 __. 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 , _,_ , _,_ -,_ 9. 2, 7, -3, 2, -8, -3, -13, -8, -18,_ __ _,_ 10. 1, 5, 12, 22, 35, _-1_ _ __
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Use inductive reasoning to predict the next number in each list. 1. 4, 8, 12, 16, 20, 24, _? 2. 5, 11, 17, 23, 29, 35,_ 3. 3, 5, 9, 15, 23, 33, _? 4. 1, 8, 27, 64, 125,_ ? 5. 1, 4, 9, 16, 25, 36, 49, _? 6. 80, 70, 61, 53, 46, 40,_ ? 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 ,_ ? 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 ,_ 9. 2, 7, −3, 2, −8, −3, −13, −8, -18, _? 10. 1, 5, 12, 22, 35, _?
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1 4,8,12,16,20,24, ? 6 80, 70, 61, 53, 46, 40, ? 2 5, 11, 17, 23, 29, 35, ? ? 7 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 , 3 3, 5, 9, 15, 23, 33, ? ? 8 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 4 1, 8, 27, 64, 125, ? 9 2, 7, −3, 2, −8, −3, −13, −8, −18, ? 5 1, 4, 9, 16, 25, 36, 49, ? 10 1, 5, 12, 22, 35, ? B. Use inductive reasoning to decide whether each statement is correct. 1 point each
In Exercises 1 to 10, use inductive reasoning to predict 14. the next number in each list. 1. 4, 8, 12, 16, 20, 24, ? 15. 2. 5, 11, 17, 23, 29, 35, ? 3. 3, 5, 9, 15, 23, 33, ? 4. 1, 8, 27, 64, 125, ? 16. 5. 1, 4, 9, 16, 25, 36, 49,? 6. 80, 70, 61, 53, 46, 40, ? 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 , ? Incli 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 , ? Gali a fal 9. 2, 7,−3, 2,−8, −3,−13, −8,−18,? fall e 10. 1, 5, 12, 22, 35, ? diffi that In Exercises 11 to 16, use inductive reasoning to decide that whether each statement is correct. Note: The numbers 1, 2, 3, ball 4, 5, ... are called counting numbers or natural numbers. obje Any counting number n divided by 2 produces a remainder deter of 0 or 1. If n / 2 has a remainder of O, then π is an even plan counting number. If n / 2 has a remainder of 1, then η is an odd counting number. time Even counting numbers: 2, 4, 6, 8, 10, ... Odd counting numbers: 1, 3, 5, 7, 9, ... 11. The sum of any two even counting numbers is always 0 an even counting number. 12. The product of an odd counting number and an even counting number is always an even counting number. 13. The product of two odd counting numbers is always an odd counting number.
EXERCISE SET 1.1 In Exercises 1 to 10, use inductive reasoning to predict 14. The sum of two odd counting numbers is always an odo the next number in each list. counting number. 1. 4, 8, l2, l6, 20, 24, ? 15. Pick any counting number. Multiply the number by 6. 2. 5, 11, 17, 23, 29, 35, ? Add 8 to the product. Divide the sum by 2. Subtract 4 from the quotient. The resulting number is twice the 3. 3,5,9,15, 23、33、? original number. 4. 1, 8, 27, 64, 125,? 16. Pick any counting number. Multiply the number by 8. 5. 1.4. 9. 16. 25. 36. 49.? Subtract 4 from the product. Divide the difference by 6. 80, 70, 61, 53, 46, 40, ? 2. Add 2 to the quotient. The resulting number is four times the original number. 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 , . ? Inclined Plane Experiments 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 , ? Galileo 1564-1642 wanted to determine how the speed of a falling object changes as it falls. He conducted many free- 9. 2, 7,−3, 2,−8, −3, −13, −8, −18, ? fall experiments, but he found the motion of a falling object 10. l, 5, l2, 22, 35, ? difficult to analyze. Eventually, he came up with the idea In Exercises 11 to 16, use inductive reasoning to decide that it would be easier to perform experiments with a ball that rolls down a gentle incline, because the speed of the whether each statement is correct. Note: The numbers 1, 2, 3, ball would be slower than the speed of a falling object. One 4, 5, ... are called counting numbers or natural numbers. objective of Galileo’s inclined plane experiments was to Any counting number n divided by 2 produces a remainder determine how the speed of a ball rolling down an inclined of 0 or 1. If n / 2 has a remainder of 0, then n is an even plane changes as it rolls. counting number. If n / 2 has a remainder of 1. then n is Examine the inclined plane shown below and the an odd counting number. time-distance data in the following table. Even counting numbers: 2, 4, 6, 8, 10, ... Odd counting numbers: 1, 3, 5, 7, 9, ... 11. The sum of any two even counting numbers is always an even counting number.Curved groove 12. The product of an odd counting number and an even counting number is always an even counting number. 13. The product of two odd counting numbers is always an odd counting number.
In Exercises 1 to 10, use inductive reasoning to predict 14. The sum of two odd counting numbers is always an odd the next number in each list. counting number. 1. 4, 8, 12, 16, 20, 24, ? 15. Pick any counting number. Multiply the number by 6. 2. 5, 11, 17, 23, 29, 35, ? Add 8 to the product. Divide the sum by 2. Subtract 4 3. 3, 5, 9,15, 23, 33, ? from the quotient. The resulting number is twice the 4. 1, 8, 27, 64, 125, ? original number. 5. 1, 4, 9, 16, 25, 36, 49, ? 16. Pick any counting number. Multiply the number by 8. 6. 80, 70, 61, 53, 46, 40,? Subtract 4 from the product. Divide the difference by 2. Add 2 to the quotient. The resulting number is four 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 , ? times the original number. Inclined Plane Experiments 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 , Galileo 1564-1642 wanted to determine how the speed of a falling object changes as it falls. He conducted many free- 9. 2, 7,−3, 2,−8,−3, −13, −8, −18,? fall experiments, but he found the motion of a falling object 10. 1, 5, 12, 22, 35, ? difficult to analyze. Eventually, he came up with the idea that it would be easier to perform experiments with a ball In Exercises 11 to 16, use inductive reasoning to decide that rolls down a gentle incline, because the speed of the whether each statement is correct. Note: The numbers 1, 2, 3, ball would be slower than the speed of a falling object. One 4, 5, ... are called counting numbers or natural numbers. objective of Galileo’s inclined plane experiments was to Any counting number n divided by 2 produces a remainder determine how the speed of a ball rolling down an inclined of 0 or 1. If n / 2 has a remainder of 0, then n is an even counting number. If n / 2 has a remainder of 1, then n is plane changes as it rolls. Examine the inclined plane shown below and the an odd counting number. time-distance data in the following table. Even counting numbers: 2, 4, 6, 8, 10, ... Starting position, Odd counting numbers: 1, 3, 5, 7, 9, ... ball at rest Position of the ball 11. The sum of any two even counting numbers is always after 4 seconds 128 centímeters an even counting number. 12. The product of an odd counting number and an even Curved groove counting number is always an even counting number. 13. The product of two odd counting numbers is always an Inclined plane 1 odd counting number.
In Exercises 1 to 10, use inductive reasoning to predict 14. The sum of two odd counting numbers is always an odd the next number in each list. counting number. 1. 4. 8, l2. I6. 20. 24. ? 15. Pick any counting number. Multiply the number by 6. 2. 5, 11, 17, 23, 29, 35, ? Add 8 to the product. Divide the sum by 2. Subtract 4 3. 3, 5, 9, 15, 23, 33, ? from the quotient. The resulting number is twice the original number. 4. 1, 8, 27, 64, 125, ? 16. Pick any counting number Multiply the number by 8. 5. 1, 4, 9, 16, 25, 36, 49,? Subtract 4 from the product. Divide the difference by 6. 80, 70, 61, 53, 46, 40, ? 2. Add 2 to the quotient. The resulting number is four times the original number. 7. 3/5 , 5/7 , 7/9 , 9/11 , 11/13 , 13/15 . ? Inclined Plane Experiments Galileo 1564-1642 wanted to determine how the speed of 8. 1/2 , 2/3 , 3/4 , 4/5 , 5/6 , 6/7 ,2, a falling object changes as it falls. He conducted many free- 9. 2, 7, −3, 2, -8, -3, -13, −8, -18, ? fall experiments, but he found the motion of a falling object difficult to analyze. Eventually, he came up with the idea 10. 1, 5, 12, 22, 35, ? that it would be easier to perform experiments with a ball # In Exercises 11 to 16, use inductive reasoning to decide that rolls down a gentle incline, because the speed of the whether each statement is correct. Note: The numbers 1, 2, 3, ball would be slower than the speed of a falling object. One 4, 5, ... are called counting numbers or natural numbers objective of Galileo’s inclined plane experiments was to Any counting number n divided by 2 produces a remainder determine how the speed of a ball rolling down an inclined of 0 or 1. If n / 2 has a remainder of O, then η is an even plane changes as it rolls. counting number. If n / 2 has a remainder of 1, then π is Examine the inclined plane shown below and the an odd counting number. time-distance data in the following table. Even counting numbers: 2, 4, 6, 8, 10, ... Starting position Odd counting numbers: 1, 3, 5, 7, 9, ... ball at rest Position of the ball 11. The sum of any two even counting numbers is always after 4 seconds 128 centimeters an even counting number. 12. The product of an odd counting number and an even 。 Curved groove counting number is always an even counting number. 13. The product of two odd counting numbers is always an Inclined plane l odd counting number.