document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175621>Question 1175621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man buys premium bonds every year . In the first year , he buys sh.2000 worth of bonds . If every year he increases his annual investments in bonds by sh.600 , how long will he take for his total investment in bonds to be sh.37000 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801279 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801279\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "His investments for each year form an arithmetic sequence:<br><BR>\n" );
document.write( "2000, 2600, 3200, 3800, 4400, 5000, 5600, 6200, 6800, ...<br><BR>\n" );
document.write( "The fastest path to the answer is to add up the successive amounts until the total reaches 37000 or more.  You will quickly find that his total investment over 8 years is less than 37000 and the total over 9 years is greater then 37000.<br><BR>\n" );
document.write( "For an algebraic solution, using the formula for the sum of an arithmetic sequence....<br><BR>\n" );
document.write( "first payment: 2000<BR>\n" );
document.write( "payment in n-th year: 2000+600(n-1) = 1400+600n<br><BR>\n" );
document.write( "Since the sequence is arithmetic, the sum of payments over n years is the number of years, multiplied by the average of the amounts from the first and last years:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+n%28%282000%2B%281400%2B600n%29%29%2F2%29+=+n%281700%2B300n%29 ALIGN=MIDDLE  ALT=\"S+=+n%28%282000%2B%281400%2B600n%29%29%2F2%29+=+n%281700%2B300n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "We want that sum to be 37000:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%281700%2B300n%29+=+37000 ALIGN=MIDDLE  ALT=\"n%281700%2B300n%29+=+37000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1700n%2B300n%5E2+=+37000 ALIGN=MIDDLE  ALT=\"1700n%2B300n%5E2+=+37000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300n%5E2%2B1700n-37000+=+0 ALIGN=MIDDLE  ALT=\"300n%5E2%2B1700n-37000+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3n%5E2%2B17n-370+=+0 ALIGN=MIDDLE  ALT=\"3n%5E2%2B17n-370+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That quadratic does not factor; you need to find the solution using the quadratic formula or a graphing calculator.  Of those two options, clearly the graphing calculator is more efficient.<br><BR>\n" );
document.write( "But you found the answer much faster by performing a few simple additions....<br><BR>\n" );
document.write( " </SPAN>\n" );
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