Draw the next figure in each sequence.

47. 
48. 
    Image Long Description

49. Reasoning Find the perimeter when 100 triangles are put together in the pattern shown. Assume that all triangle sides are 1 cm long.

    

50. Think About a Plan Below are 15 points. Most of the points fit a pattern. Which does not? Explain.

    A ( 6 , − 2 ) B ( 6 , 5 ) C ( 8 , 0 ) D ( 8 , 7 ) E ( 10 , 2 ) F ( 10 , 6 ) G ( 11 , 4 ) H ( 12 , 3 ) I ( 4 , 0 ) J ( 7 , 6 ) K ( 5 , 6 ) L ( 4 , 7 ) M ( 2 , 2 ) N ( 1 , 4 ) O ( 2 , 6 ) eh open 6 comma negative 2 close b open 6 comma 5 close c open 8 comma 0 close d open 8 comma 7 close e open 10 comma 2 close f open 10 comma 6 close g open 11 comma 4 close h open 12 comma 3 close i open 4 comma 0 close j open 7 comma 6 close k open 5 comma 6 close l open 4 comma 7 close m open 2 comma 2 close n open 1 comma 4 close o open 2 comma 6 close

    • How can you draw a diagram to help you find a pattern?
    • What pattern do the majority of the points fit?
51. Language Look for a pattern in the Chinese number system.

    Chinese Number System

    Number	Chinese Word
    1	yī
    2	èr
    3	sān
    4	sì
    5	wŭ
    6	lìu
    7	qī
    8	bā
    9	jĭu
    10	shí
    11	shí-yī
    12	shí-èr
    ⋮	⋮
    20	èr-shí
    21	èr-shí-yī
    ⋮	⋮
    30	sān-shí

    1. What is the Chinese name for the numbers 43, 67, and 84?
    2. Reasoning Do you think that the Chinese number system is base 10? Explain.
52. Open-Ended Write two different number sequences that begin with the same two numbers.
53. Error Analysis For each of the past four years, Paulo has grown 2 in. every year. He is now 16 years old and is 5 ft 10 in. tall. He figures that when he is 22 years old he will be 6 ft 10 in. tall. What would you tell Paulo about his conjecture?
54. Bird Migration During bird migration, volunteers get up early on Bird Day to record the number of bird species they observe in their community during a 24-h period. Results are posted online to help scientists and students track the migration.

    Bird Count

    Year	Number of Species
    2004	70
    2005	83
    2006	80
    2007	85
    2008	90

    1. Make a graph of the data.
    2. Use the graph and inductive reasoning to make a conjecture about the number of bird species the volunteers in this community will observe in 2015.
55. Writing Describe a real-life situation in which you recently used inductive reasoning.

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