document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=307358>Question 307358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to complete the pattern...HELP!!!  Thanks so much for your help!\r<BR>\n" );
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document.write( "x.....y\r<BR>\n" );
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document.write( "1.....0<BR>\n" );
document.write( "2.....2<BR>\n" );
document.write( "4.....12<BR>\n" );
document.write( "5......20<BR>\n" );
document.write( "10....90<BR>\n" );
document.write( "___....380<BR>\n" );
document.write( "___....870<BR>\n" );
document.write( "___....30<BR>\n" );
document.write( "___....42\r<BR>\n" );
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document.write( "y = ______ </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #219880 by </B><A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><B>vksarvepalli(154)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=vksarvepalli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=219880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> General note:\r<BR>\n" );
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document.write( "keep it mind that in series or this type of function problems,first observe the question carefully,don't rush and start writing equations and all \r<BR>\n" );
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document.write( "if we get that pattern then its done.we can do also this problem by assuming it is a 2nd degree equation taking some constants and then substituting the given values and finding out the unknown constants.\r<BR>\n" );
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document.write( "like we can assume the relation to be y=ax^2+bx+c or y=ax^3+bx^2+cx+d since we got 5 pairs of x&y with us we can even go for a 4th degree equation,but imagine how tedious the problem becomes.\r<BR>\n" );
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document.write( "so, here if we observe that \r<BR>\n" );
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document.write( "when x=1, y=0 that is lets say 1x0 or 1x(1-1)<BR>\n" );
document.write( "when x=2, y=1 that may be say  2x1 or 2x(2-1)<BR>\n" );
document.write( "when x=4, y=12                 4x3 or 4x(4-1)\r<BR>\n" );
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document.write( "by now we can say that the pattern is\r<BR>\n" );
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document.write( "              <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%28x-1%29+ ALIGN=MIDDLE  ALT=\"y=x%28x-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "put x=10 we get y= 90 which is verified.\r<BR>\n" );
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document.write( "so for y=380   x=20\r<BR>\n" );
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document.write( "20....380<BR>\n" );
document.write( "30....870<BR>\n" );
document.write( "6....30<BR>\n" );
document.write( "7....42<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );