i need help with a math pattern

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i need help with a math pattern

Mathematics
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fibonnacci?
no, it's an algebra pattern question about terms of a pattern
it might be useful if you give us the question so that we have a better understanding of it

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

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