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Math Help - series and sequences

  1. #1
    Junior Member
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    series and sequences

    A piece of wire (ABCDEF…) is used to make a pattern formed from many concentric semi-circular arcs, AB, CD, EF… joined by short intervals BC, DE, FG… The diameter of the smallest semi-circles is 8cm and each interval is 3cm.
    i) What is the length of the 20th semi-circular arc?
    ii) How much wire is needed to form a pattern containing 20 semi-circular arcs?

    (The diagram looks like a rainbow)


    This question has really confused me and i would greatly appreciate some help, the answers are 61pi (cm) and 650pi + 57


    thank you to anyone who can help
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  2. #2
    MHF Contributor

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    Quote Originally Posted by christina View Post
    A piece of wire (ABCDEF…) is used to make a pattern formed from many concentric semi-circular arcs, AB, CD, EF… joined by short intervals BC, DE, FG… The diameter of the smallest semi-circles is 8cm and each interval is 3cm.
    i) What is the length of the 20th semi-circular arc?
    ii) How much wire is needed to form a pattern containing 20 semi-circular arcs?

    (The diagram looks like a rainbow)


    This question has really confused me and i would greatly appreciate some help, the answers are 61pi (cm) and 650pi + 57


    thank you to anyone who can help
    Just take it in steps: what is the radius of the first arc? (4), of the second arc? (4+3), of the third arc? (4+3+3), thus the radius of the twentieth arc is...

    For the second question, the length of short intervals should be simple (they have same length, and there are xxx of them); and for the length of the arcs, you have to sum the lengths of the 20 first arcs (this is the sum of a geometric progression, you may know a formula for that).
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