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Math Help - A bank account...

  1. #1
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    A bank account...

    a bank account pays 3% interest. Suppose you invest $2000 in such an account.
    Let a(n) be the amount in the account after n years. So a1=2000+0.03*2000=2060 and a2=2060+0.03*2060=2121.80. Find a3 and a4?

    Is this sequence an arithmetic sequence, geometric sequence or neither? and why?


    Find a10
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  2. #2
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    Cool

    well i know it is not arithmetic but i'm not so sure about what exactly, and is this simple or compound interest
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  3. #3
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    Hello,

    Quote Originally Posted by gumi View Post
    a bank account pays 3% interest. Suppose you invest $2000 in such an account.
    Let a(n) be the amount in the account after n years. So a1=2000+0.03*2000=2060 and a2=2060+0.03*2060=2121.80. Find a3 and a4?

    Is this sequence an arithmetic sequence, geometric sequence or neither? and why?


    Find a10
    You should see it this way :

    a_1=2000+0.03*2000=2000(1+0.03)=2000*1.03

    a_2=(2000*1.03)+(2000*1.03)*0.03=(2000*1.03)(1+0.0  3)=2000*1.03^2

    It's a geometric sequence
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  4. #4
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    since a2 uses a1 in it's equation, it makes it a geometric sequence.
    You can see the difference between the two here:
    Arithmetic and Geometric series

    It's compound interest since you're taking 3% of whatever the last total is and not just 3% of the initial amount
    a3 is easy: 2121.80+0.03*2121.80 = 2185.45
    You could just write it as 2121.80*1.03, or even 2000*1.03^3

    The series is 2000*1.03^n where n = years in account.
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