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Practice 1-1 Patterns and Inductive Reasoning

This document contains the work of a student named Julie Ann Obias for their Practice 1-1 assignment on patterns and inductive reasoning. The assignment contains multiple pattern identification, extension, and formula questions. Key details include identifying patterns of increasing by 6, decreasing by 0.00001, doubling, and the Fibonacci sequence. Formulas are provided for the number of handshakes with n people and the successive ratio in the Fibonacci sequence.

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Willy Clemente
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542 views2 pages

Practice 1-1 Patterns and Inductive Reasoning

This document contains the work of a student named Julie Ann Obias for their Practice 1-1 assignment on patterns and inductive reasoning. The assignment contains multiple pattern identification, extension, and formula questions. Key details include identifying patterns of increasing by 6, decreasing by 0.00001, doubling, and the Fibonacci sequence. Formulas are provided for the number of handshakes with n people and the successive ratio in the Fibonacci sequence.

Uploaded by

Willy Clemente
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Name: Julie ann Obias Class: BSBA 2-Marketing Date: November 11, 2020

Practice 1-1 Patterns and Inductive Reasoning


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

1. 17, 23, 29, 35, 41, . . . 47, 53 2. 1.01, 1.001, 1.0001, . . . 1.00001, 1.00001

3. 12, 14, 18, 24, 32, . . . 42, 54 4. 2, -4, 8, -16, 32, . . . -64, 128

5. 1, 2, 4, 7, 11, 16, . . . 22, 29 6. 32, 48, 56, 60, 62, 63, . . . 63.5, 63.75

Name two different ways to continue each pattern.

7. 1, 1, 2, 2 or 3 8. 48, 49, 50, 49 or 51

9. 2, 4, 6 or 8 10. A, B, C,... ,Z, A or AA

11. D, E, F, D or G 12. A, Z, B, Y or A

Draw the next figure in each sequence.

13. ___________________

14. ___________________

15. 90* 135* 157.5* 168.75*

____________________

(“ * ” symbol means degrees)


Seven people meet and shake hands with one another.

16. How many handshakes occur? There’s have a 21 handshakes

17. Using inductive reasoning, write a formula for the number of handshakes if
the number of people
is n. h = n(n-1)
2

The Fibonacci sequence consists of the pattern 1, 1, 2, 3, 5, 8, 13, . . . 21, 34

18. What is the ninth term in the pattern? The ninth term in the pattern is 34.
Why? Because the next number is found by adding up the two numbers before it.
Example: the next number in the sequence above is 21+34 = 55.
19. Using your calculator, look at the successive ratios of one term to the next.
Make a conjecture.
8/5 = 1.6
13/8 = 1.625
21/13 = 1.615384615
34/21 = 1.619047619
conclusion:
the ratio = (1 + sqrt(5))/2 approximately

20. List the first eight terms of the sequence formed by finding the differences of
successive terms in the Fibonacci sequence.
These are the first eight terms of the sequence formed of Fibonacci sequence :
0, 1, 1, 2, 3, 5, 8, 13

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