document.write( "Question 156348: Trying to find the series for my son's \"Chicago Math\" 7th grade class. It's an exponetial series with the following (x,y) points (1,1), (2,3), (3,6), (4,10), (nth,?).\r
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Algebra.Com's Answer #115170 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
I was looking at this problem trying to \"see\" the series.
\n" ); document.write( "I don't see it as an \"exponential\" series.
\n" ); document.write( "What I do see is that each y-value is the sum of all the previous x-values.
\n" ); document.write( "This can be expressed as:
\n" ); document.write( " $\"highlight%28y+=+%28%28x%5E2%2Bx%29%29%2F2%29\"$
\n" ); document.write( "To try a few values: x = 1:
\n" ); document.write( " $\"y+=+%281%5E2%2B1%29%2F2\"$
\n" ); document.write( " $\"y+=+%281%2B1%29%2F2\"$
\n" ); document.write( " $\"y+=+1\"$
\n" ); document.write( "For x = 3:
\n" ); document.write( " $\"y+=+%283%5E2%2B3%29%2F2\"$
\n" ); document.write( " $\"y+=+%289%2B3%29%2F2\"$
\n" ); document.write( " $\"y+=+12%2F2\"$
\n" ); document.write( " $\"y+=+6\"$
\n" ); document.write( "For x = 4:
\n" ); document.write( " $\"y+=+%284%5E2%2B4%29%2F2\"$
\n" ); document.write( " $\"y+=+%2816%2B4%29%2F2\"$
\n" ); document.write( " $\"y+=+20%2F2\"$
\n" ); document.write( " $\"y+=+10\"$
\n" ); document.write( "So on this basis, the nth term would be:
\n" ); document.write( " $\"highlight%28y%5Bn%5D+=+%28%28n%5E2%2Bn%29%29%2F2%29\"$ \n" ); document.write( "

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