document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204430>Question 1204430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man borrows 1,000 and agrees to repay with 10 instalments, each instalment being less than the preceding instalment by 8. Find the his first instalment  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840687 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840687\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "a = first installment = first term of arithmetic sequence\r<BR>\n" );
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document.write( "n = 10 = number of payments<BR>\n" );
document.write( "d = -8 = common difference\r<BR>\n" );
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document.write( "Sn = sum of first n terms of arithmetic sequence, aka arithmetic progression (AP)<BR>\n" );
document.write( "Sn = 1000\r<BR>\n" );
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document.write( "Sn = (n/2)*(2*a + d(n-1))<BR>\n" );
document.write( "1000 = (10/2)*(2*a - 8(10-1))<BR>\n" );
document.write( "1000 = 5(2a-72)<BR>\n" );
document.write( "2a-72 = 1000/5<BR>\n" );
document.write( "2a-72 = 200<BR>\n" );
document.write( "2a = 200+72<BR>\n" );
document.write( "2a = 272<BR>\n" );
document.write( "a = 272/2<BR>\n" );
document.write( "a = 136\r<BR>\n" );
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document.write( "The arithmetic sequence of 10 payments is<BR>\n" );
document.write( "136, 128, 120, 112, 104, 96, 88, 80, 72, 64<BR>\n" );
document.write( "I used the \"sequence\" command in GeoGebra to generate this list quickly. A spreadsheet is another good option.\r<BR>\n" );
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document.write( "As a check,<BR>\n" );
document.write( "136+128+120+112+104+96+88+80+72+64 = 1000<BR>\n" );
document.write( "We have confirmed the correct first payment.<BR>\n" );
document.write( "An interesting thing to notice is:  <BR>\n" );
document.write( "(n/2)*(1st term + 10th term) = (10/2)*(136+64) = 1000\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>136</font><BR>\n" );
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