anonymous
  • anonymous
i need help with a math pattern
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
fibonnacci?
anonymous
  • anonymous
no, it's an algebra pattern question about terms of a pattern
amistre64
  • amistre64
it might be useful if you give us the question so that we have a better understanding of it

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anonymous
  • anonymous
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.
amistre64
  • amistre64
well, there are 2 sequence summations that we can use; and arithmatic and a geometric
anonymous
  • anonymous
we haven't been doing geometry, so it's probably the arithmatic
amistre64
  • amistre64
\[\sum_{n=1}^{50}a_1+d(n-1)=\frac{50(a_1+a_{50})}{2}\]
amistre64
  • amistre64
\[\sum_{n=1}^{50}a^1*r^{n-1}=a_1\frac{1-r^50}{1-r}\]
anonymous
  • anonymous
this is a 6th grade homework question
amistre64
  • amistre64
r^(50) that is; forgot to wrap it in a {}
anonymous
  • anonymous
i'm not following you
amistre64
  • amistre64
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?
anonymous
  • anonymous
ok, thanks for your help. so then we could set any number as the first term and go from there?
amistre64
  • amistre64
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
anonymous
  • anonymous
ok, that works. thanks again
amistre64
  • amistre64
\[a_{80}=a_1+d(80-1)\]

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