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anonymous

  • 4 years ago

i need help with a math pattern

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  1. amistre64
    • 4 years ago
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    fibonnacci?

  2. anonymous
    • 4 years ago
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    no, it's an algebra pattern question about terms of a pattern

  3. amistre64
    • 4 years ago
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    it might be useful if you give us the question so that we have a better understanding of it

  4. anonymous
    • 4 years ago
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    Here's the question: The first 50 terms of a pattern sum to 2000. a) Describe the pattern. b) Describe how you found the sum. c) Give the 100th term of the pattern. d) List all the patterns that you found.

  5. amistre64
    • 4 years ago
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    well, there are 2 sequence summations that we can use; and arithmatic and a geometric

  6. anonymous
    • 4 years ago
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    we haven't been doing geometry, so it's probably the arithmatic

  7. amistre64
    • 4 years ago
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    \[\sum_{n=1}^{50}a_1+d(n-1)=\frac{50(a_1+a_{50})}{2}\]

  8. amistre64
    • 4 years ago
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    \[\sum_{n=1}^{50}a^1*r^{n-1}=a_1\frac{1-r^50}{1-r}\]

  9. anonymous
    • 4 years ago
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    this is a 6th grade homework question

  10. amistre64
    • 4 years ago
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    r^(50) that is; forgot to wrap it in a {}

  11. anonymous
    • 4 years ago
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    i'm not following you

  12. amistre64
    • 4 years ago
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    lets do arith then :) \[\frac{50(a_1+a_{50})}{2}=2000\] \[{25(a_1+a_{50})}{}=2000\] \[{a_1+a_{50}}{}=2000/25\] \[{a_1+a_{50}}{}=80\] sound good?

  13. anonymous
    • 4 years ago
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    ok, thanks for your help. so then we could set any number as the first term and go from there?

  14. amistre64
    • 4 years ago
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    correct; choose any 2 numbers that add up to 80; and work in the summation rule for the rest of it to get the details of the common difference

  15. anonymous
    • 4 years ago
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    ok, that works. thanks again

  16. amistre64
    • 4 years ago
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    \[a_{80}=a_1+d(80-1)\]

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