document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=922257>Question 922257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sum of 6 consecutive even numbers is 618. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #559454 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=559454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> MENTAL MATH (if you just need a quick answer):<BR>\n" );
document.write( "The number in the middle of those 6 consecutive even numbers is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=618%2F6=103 ALIGN=MIDDLE  ALT=\"618%2F6=103\"   DISABLED_style= \"max-width:90%; height:auto;\" > . (It is the average and the median of the 6 consecutive even numbers, because they form an arithmetic sequence. If you learned about arithmetic sequences, you may have been taught that).<BR>\n" );
document.write( "The 6 consecutive even numbers are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2898%29 ALIGN=MIDDLE  ALT=\"highlight%2898%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28100%29 ALIGN=MIDDLE  ALT=\"highlight%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28102%29 ALIGN=MIDDLE  ALT=\"highlight%28102%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28104%29 ALIGN=MIDDLE  ALT=\"highlight%28104%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28106%29 ALIGN=MIDDLE  ALT=\"highlight%28106%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28108%29 ALIGN=MIDDLE  ALT=\"highlight%28108%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "SHOWING YOUR WORK (with lots of explanations):<BR>\n" );
document.write( "First, you define a variable in the most convenient way you can think of.<BR>\n" );
document.write( "You do not need to call one of your even numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2k ALIGN=MIDDLE  ALT=\"2k\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" >= an integer to show that it is an even number.<BR>\n" );
document.write( "You can call one of those 6 even numbers <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and when you solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > , check if it is an even number. If the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > you find is not even, there is no solution.<BR>\n" );
document.write( "One option is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the smallest of the 6 consecutive even numbers.<BR>\n" );
document.write( "If you learned about arithmetic sequences, you can try to use some formulas from that, but it may be more trouble than it's worth.<BR>\n" );
document.write( "If the smallest even integer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the other 5 even numbers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B2 ALIGN=MIDDLE  ALT=\"n%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B4 ALIGN=MIDDLE  ALT=\"n%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B6 ALIGN=MIDDLE  ALT=\"n%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B8 ALIGN=MIDDLE  ALT=\"n%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B10 ALIGN=MIDDLE  ALT=\"n%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The sum is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B%28n%2B2%29%2B%28n%2B4%29%2B%28n%2B6%29%2B%28n%2B8%29%2B%28n%2B10%29=n%2Bn%2B2%2Bn%2B4%2Bn%2B6%2Bn%2B8%2Bn%2B10=6n%2B30 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6n%2B30=618 ALIGN=MIDDLE  ALT=\"6n%2B30=618\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6n=618-30 ALIGN=MIDDLE  ALT=\"6n=618-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6n=588 ALIGN=MIDDLE  ALT=\"6n=588\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=588%2F6 ALIGN=MIDDLE  ALT=\"n=588%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28n=98%29 ALIGN=MIDDLE  ALT=\"highlight%28n=98%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Another option would be saying that the 6 consecutive even numbers are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5 ALIGN=MIDDLE  ALT=\"x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B5 ALIGN=MIDDLE  ALT=\"x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The difference between one and the next is 2, so they are either 6 consecutive even numbers, or 6 consecutive odd numbers.<BR>\n" );
document.write( "Their sum is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%2B%28x-3%29%2B%28x-1%29%2B%28x%2B1%29%2B%28x%2B3%29%2B%28x%2B5%29=x-5%2Bx-3%2Bx-1%2Bx%2B1%2Bx%2B3%2Bx%2B5=6x ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x=618 ALIGN=MIDDLE  ALT=\"6x=618\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=618%2F6 ALIGN=MIDDLE  ALT=\"x=618%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=103 ALIGN=MIDDLE  ALT=\"x=103\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5=103-5=98 ALIGN=MIDDLE  ALT=\"x-5=103-5=98\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );