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Math Help - Sequences, Series, etc.

  1. #1
    Junior Member
    Joined
    Nov 2009
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    54

    Exclamation Sequences, Series, etc.

    1) A tree is 10 m tall and grew 180 cm last year. Its height increases each year by 80% of the previous year's growth. Find the height of the tree five years from now and the ultimate height of the tree.

    2) Pat borrows $30000 at 9% pa reducible montly to be repaid in 60 equal montly instalments of $622.75. With the 12th payment, Pat repays an extra $5000. After this payments continue at $622.75 per motnh. How many more repayments will be needed?

    I got these questions completely wrong during the exams Could someone please show me how to do them?
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  2. #2
    MHF Contributor
    Joined
    Apr 2008
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    1,092
    1. The ultimate height of the tree in meters:

    10 + 0.18 \sum_{n=1}^\infty 0.8^n
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