Find a pattern for each sequence. Use inductive reasoning to show the next two terms. 1. 5, 10, 20, 40, . . . 2. 1, 4, 9, 16, 25, . . . 3. 1, -1,2, -2, 3, .. . 1 1 1 4. 1, 2 1 8 .. . 5. 1, 7 3 7 -. . 6. 15, 12, 9, 6, .. . Use the sequence and inductive reasoning to make a conjecture. 8. What are the coordinates of the point in the 8th figure in the sequence? 7. What is the 12th figure in the sequence? O.G.Q.O 1 2 . - 5 ) Make a conjecture for each scenario. Show your work. 9. The sum of the first 100 even numbers To start, find the first few terms of the sequence and look for a pattern. 2=2 =1 x 2 2+4=6 =2 X 2+4+ =3 x 2+4+6+ x Conjecture: Sum of the first 100 even numbers = 10. The product of an even and odd number Find one counterexample to show that each conjecture is false. 11. 41 and 42 are supplementary, so one of the angles is acute. 12. AABC is a right triangle, so ZA measures 90. 13. The sum of two numbers is greater than either number. 14. The difference of two integers is less than either integer. Draw the next figure in each sequence