Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find a pattern for each sequence. Use the pattern to show the next two terms.

6. 5, 10, 20, 40,…
7. 1, 4, 9, 16, 25,…
8. 1 , − 1 , 2 , − 2 , 3 , … 1 comma negative 1 comma 2 comma negative 2 comma 3 comma dot dot dot
9. 1 , 1 2 , 1 4 , 1 8 , … 1 comma . 1 half , comma , 1 fourth , comma , 1 eighth , comma dot dot dot
10. 1 , 1 2 , 1 3 , 1 4 , … 1 comma . 1 half , comma , 1 third , comma , 1 fourth , comma dot dot dot
11. 15, 12, 9, 6,…
12. O, T, T, F, F, S, S, E,…
13. J, F, M, A, M,…
14. 1, 2, 6, 24, 120,…
15. Washington, Adams, Jefferson,…
16. dollar coin, half dollar, quarter,…
17. AL, AK, AZ, AR, CA,…
18. Aquarius, Pisces, Aries, Taurus,…
19. 
    Image Long Description
20. 

See Problem 2.

Use the sequence and inductive reasoning to make a conjecture.

21. What is the color of the fifteenth figure?
22. What is the shape of the twelfth figure?
23. What is the color of the thirtieth figure?
24. What is the shape of the fortieth figure?

See Problem 3.

Make a conjecture for each scenario. Show your work.

25. the sum of the first 100 positive odd numbers
26. the sum of the first 100 positive even numbers
27. the sum of two odd numbers
28. the sum of an even and odd number
29. the product of two even numbers
30. the product of two odd numbers

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