Practice inductive reasoning

1. Inductive Reasoning 1 2 3 4 5 6 … n … 20 0 3 10 21 36 55 … ? … ?

2. Sequences Terms: 4, 5, 6, 7, 8 … Terms: A, C, E, G, …

3. Find the next 2 terms. 2, 4, 6, 8, 10, ___, ____ 5, 10, 15, 20, 25, ___, ____ 4, 8, 12, 16, 20, ___, ____ Add two to the previous term. 12 14 Add 4 to the previous term. 24 28 30 35 Add 5 to the previous term.

4. Find the next 2 terms. 1, 3, 5, 7, 9, ___, ____ 3, 5, 7, 9, 11, ___, ____ 1, 4, 9, 16, 25, ___, ____ Add 2 to the previous term. Add 3, 5, 7, 9, ... 11 13 36 49 13 15 Add 2 to the previous term.

5. Find the next 2 terms. 1, .5, .33, .25, ____, ____ 1, 8, 27, 64, ____, ____ 10, 5, 2.5, 1.25, ____, ____ .2 .166 .625 .3125 125 216 Perfect cubes of the counting numbers Half the previous term

6. Find the next 2 terms. 10, 21, 32, 43, ____, ____ 16, 25, 36, 49, ____, ____ 15, 19, 23, 27, ____, ____ 54 65 31 35 64 81 Add 11 to the previous term. Add 4 to the previous term. Add 9, 11, 13, 15, 17 …

7. Find the next 2 terms. 9, 16, 21, 24, ____, ____ 16, 17, 19, 22, ____, ____ 3, 32, 321, 3213, ____, ____ 25 24 32132 321321 26 31 Add 7, 5, 3, 1, -1, -3 … 3, 32, 321, and repeat as add on. Add 1, add 2, add 3, …

8. Weird Sequences A, C, E, G, ___ 1, 2, 3, 5, 8, 13, ___ O, T, T, F, F, S, S, E, ___ I N 21 Skip every other letter First letter of each counting number Fibbonacci Sequence: Add the previous 2 terms.

9. Weird Sequences 0, .5, .67, .75, .8, ____ 1, 1.141, 1.73, 2, 8, 2.24, ___ 4, 6, 8, 9, 10, 12, 14, ___ .833 11 13 16 Add 2, then 2, then 1, then 1, then 2, then 2, …

10. Weird Sequences 1, 2, 5, 20, 50, 100, ____ A, E, F, H, I, K, L, M, ___ A, K, Q, J, ___ 200 10 N Numbers on dollar bills. Letters that are not curved. Add 2 to the previous term.

11. Weird Sequences 8, 5, 4, 9, 1, 7, 6, ____ B, C, D, G, J, ___ 60, 90, 108, 120, ___ 3 O 128.6 digits in alphabetical order Curved letters Interior angles of regular polygons

12. Summary Sometimes the gaps between terms are constant. Sometimes the gaps between terms increase at a pattern. Sometimes the next term is a multiple of the previous term. If so, this can be seen by dividing a term by the previous term.

13. Summary The purpose of these exercises is to get practice at recognizing patterns. Sometimes the patterns are bizzare. It is not necessary to be able to find all the patter.

14. C’est fini. Good day and good luck. A Senior Citizen Production That’s all folks.

15. C’est fini. Good day and good luck.