document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=859811>Question 859811</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given two different arithmetic sequences 3,14,25,36 (obviously increasing by 11)<BR>\n" );
document.write( "and 2,9,16,23 (obviously increasing by 7).  What are the first 10 numbers which appear in both sequences ?\r<BR>\n" );
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document.write( "One tutor answered it with a solution that I had already done (the long way) which is simply to \"keep adding 11 and 7 until you have 10 terms that match.  All of which is true, but isn't there a formula that can be used to solve it a different way? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517969 by </B><A HREF=/tutors/aboutme.mpl?userid=richwmiller><B>richwmiller(17219)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richwmiller><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=richwmiller><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=517969\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An = A1 + (n - 1)d<BR>\n" );
document.write( "An=3 + 11(n - 1)<BR>\n" );
document.write( "An=2 + 7(n - 1)<BR>\n" );
document.write( "You might think that by setting them equal you would get at least the first matching number but you don't.\r<BR>\n" );
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document.write( "3 + 11(n - 1)= 2 + 7(n - 1)<BR>\n" );
document.write( "and solve for n<BR>\n" );
document.write( "3-11n-11=2+7n-7<BR>\n" );
document.write( "11n-8=7n-5<BR>\n" );
document.write( "4n=3<BR>\n" );
document.write( "n=3/4<BR>\n" );
document.write( "The problem seems to be that the matching numbers don't occur at the same place in the sequence so n is not the same for both. They never coincide in the same place.\r<BR>\n" );
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document.write( "3 + 11(x - 1)= 2 + 7(y - 1)<BR>\n" );
document.write( "The solution pattern is<BR>\n" );
document.write( "x = 7a+6 and y = 11a+9 <BR>\n" );
document.write( "now just pick your a and solve for x and y<BR>\n" );
document.write( "the first solution with a=1 is<BR>\n" );
document.write( "x = 13 and y = 20\r<BR>\n" );
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document.write( "Ax=3 + 11(x - 1)<BR>\n" );
document.write( "Ay=2 + 7(y - 1)<BR>\n" );
document.write( "Ax=Ay<BR>\n" );
document.write( "and then plug those into the formula.<BR>\n" );
document.write( "Ax=3 + 11(x - 1):3+11*12=135<BR>\n" );
document.write( "Ay=2 + 7(y - 1) : 2+7*19=135\r<BR>\n" );
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document.write( "when a=2<BR>\n" );
document.write( "x = 7a+6 and y = 11a+9 <BR>\n" );
document.write( "x=20 y=31<BR>\n" );
document.write( "Ax=3 + 11(x - 1):3+11*19=212<BR>\n" );
document.write( "Ay=2 + 7(y - 1)=2+210=212<BR>\n" );
document.write( "and so on till you have your ten matches.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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