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In Exercises 1-6, describe the pattern. Then write or draw the next two numbers, letters, or figures. (See Example 1.) 1. 1. 2. 3. 4. 5.... 3. Z, Y. X, W, V,... ▶5. 6. 2. 0. 2, 6, 12, 20, ... 4. A.D. G. J, M,.... 2

In Exercises 1-6, describe the pattern. Then write or draw the next two numbers, letters, or figures. (See Example 1.) 1. 1. 2. 3. 4. 5.... 3. Z, Y. X, W, V,... ▶5. 6. 2. 0. 2, 6, 12, 20, ... 4. A.D. G. J, M,.... 2

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Mathematical Patterns and Logic Puzzles** **In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.** *(See Example 1.)* 1. 1, –2, –3, –4, … 2. 0, 1, 2, 6, 12, 20, … 3. Y, X, W, V, … 4. A, D, G, J, M, … *Figures:* 5. Sequence of shapes including a pentagon, a hexagon, and an overlapping hexagon. Next: two hexagons. 6. Sequence showing stacks of cubes. Next: two larger cubes. **In Exercises 7–10, make and test a conjecture about the given quantity.** *(See Example 2.)* 7. The sum of an even integer and an odd integer. 8. The product of any two even integers. 9. The quotient of a number and its reciprocal. 10. The quotient of two negative integers. **In Exercises 11–14, find a counterexample to show that the conjecture is false.** *(See Example 3.)* 11. The product of two positive numbers is always greater than either number. 12. If n is a nonzero integer, then \( n + \frac{1}{n} \) is always greater than 1. 13. If two angles are supplements of each other, then one of the angles must be acute. 14. A line divides \( \overline{MN} \) into two line segments. So, the line is a segment bisector of \( \overline{MN} \). **In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given information, if possible.** *(See Example 4.)* 15. If you download a GIF, then your device crashes. You download a GIF. 16. If you go to the game, then you will go to the park. You will go to the game. 17. If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles. 18. If a point divides a line segment into two congruent line segments, then the point is a midpoint. Point P divides \(\overline{FH}\) into two
Transcribed Image Text:**Mathematical Patterns and Logic Puzzles** **In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.** *(See Example 1.)* 1. 1, –2, –3, –4, … 2. 0, 1, 2, 6, 12, 20, … 3. Y, X, W, V, … 4. A, D, G, J, M, … *Figures:* 5. Sequence of shapes including a pentagon, a hexagon, and an overlapping hexagon. Next: two hexagons. 6. Sequence showing stacks of cubes. Next: two larger cubes. **In Exercises 7–10, make and test a conjecture about the given quantity.** *(See Example 2.)* 7. The sum of an even integer and an odd integer. 8. The product of any two even integers. 9. The quotient of a number and its reciprocal. 10. The quotient of two negative integers. **In Exercises 11–14, find a counterexample to show that the conjecture is false.** *(See Example 3.)* 11. The product of two positive numbers is always greater than either number. 12. If n is a nonzero integer, then \( n + \frac{1}{n} \) is always greater than 1. 13. If two angles are supplements of each other, then one of the angles must be acute. 14. A line divides \( \overline{MN} \) into two line segments. So, the line is a segment bisector of \( \overline{MN} \). **In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given information, if possible.** *(See Example 4.)* 15. If you download a GIF, then your device crashes. You download a GIF. 16. If you go to the game, then you will go to the park. You will go to the game. 17. If a quadrilateral is a square, then it has four right angles. Quadrilateral QRST has four right angles. 18. If a point divides a line segment into two congruent line segments, then the point is a midpoint. Point P divides \(\overline{FH}\) into two
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