document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075313>Question 1075313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> determine the value of m so that 2m+1, m, and 5-3m form an arithmetic progression </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #689995 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=689995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if it's an arithmetic progression, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An = A1 + (n-1)* d\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this means that A2 = A1 + d and A3 = A1 + 2d\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "based on this, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A2 - A1 = A1 + d - A1 = d\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A3 - A2 = A1 + 2d - A1 - d which results in A3 - A2 = d\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, you have:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A2 - A1 = d<BR>\n" );
document.write( "A3 - A1 = d\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in other words, the common difference is d and each succeeding term in the sequence is increased by the same value of d and each term subtracted from the term immediately above is is equal to d.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your terms are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A1 = 2m + 1<BR>\n" );
document.write( "A2 = m<BR>\n" );
document.write( "A3 = 5 - 3m\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A2 - A1 is therefore equal to m - 2m - 1 which is equal to -m - 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A3 - A2 is therefore equal to 5 - 3m - m which is equal to 5 - 4m\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since both -m - 1 and 5 - 4m are equal to d, then they are equal to each other and you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-m - 1 = 5 - 4m\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add 4m to both sides and add 1 to both sides sand you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3m = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for m to get m = 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "check your sequence is if it correct using m = 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "our sequence will be:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A1 = 2m + 1 = 4 + 1 = 5<BR>\n" );
document.write( "A2 = m = 2<BR>\n" );
document.write( "A3 = 5 - 3m = 5- 6 = -1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your arithmetic sequence is 5, 2, -1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your common difference is -3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "everything checks out ok when m = 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );