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Math Help - Problem Involving Arithmetic progression

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    Problem Involving Arithmetic progression

    Diagram shows the waves formed when a stone is thrown into the water.each wave has the shape of a circle and is r cm away from the one before it.

    a)show that the circumferences of the waves form an arithmetic progression and find the common difference.

    b)If the radius if the smallest wave is 4cm , find the radius of the tenth wave.Hence,find its circumference in term of \pi
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  2. #2
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    Quote Originally Posted by mastermin346 View Post
    Diagram shows the waves formed when a stone is thrown into the water.each wave has the shape of a circle and is r cm away from the one before it.

    a)show that the circumferences of the waves form an arithmetic progression and find the common difference.

    b)If the radius if the smallest wave is 4cm , find the radius of the tenth wave.Hence,find its circumference in term of \pi

    Hi mastermin346,

    (a)

    The radius of the inner circle is r cm. C=2\pi r
    The radius of the middle circle is 2r cm. C=4 \pi r
    The radius of the outer circle is 3r cm. C=6 \pi r

    The circumferences form an arithmetic progression with a common difference of 2 \pi r


    (b)

    The radius of the inner circle is 4 cm. C=8\pi
    The radius of the middle circle is 8 cm. C=16 \pi
    The radius of the outer circle is 12 cm. C=24 \pi

    The common difference in the sequence of circumferences 8\pi,\: 16\pi,\: 24\pi, \:. . . is 8\pi

    The common difference in the radius sequence of 4, 8, 12,..... is 4

    To find the radius of the 10th circle use r_{10}=r_1+(n-1)d

    r_{10}=4+(10-1)4

    r_{10}=40

    Use this radius of the 10th circle to compute the circumference: C=\pi D

    C=80 \pi



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