document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=890214>Question 890214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please Help. Solve Problem by writing the first few terms of a sequence.  anne borrows $1000 and agrees to pay $100 plus interest of 1% on the unpaid balance each month. find the payments for the first six months and the remaining debt at the end of that period. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #538796 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=538796\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if i understand this correctly, this is the sequence that will happen.\r<BR>\n" );
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document.write( "you borrow 1000<BR>\n" );
document.write( "at the endof the first month, the remaining balance is equal to 1.01 * 1000 which is equal to 1010.<BR>\n" );
document.write( "you pay 110 and the remaining balance is now 900.<BR>\n" );
document.write( "at the end of the next month, the remaining balance is equal to 1.01 * 900 which is equal to 909.<BR>\n" );
document.write( "you pay 109 and the remaining balance is now 800.<BR>\n" );
document.write( "at the end of the nextg month, the remaining balance is equal to 1.01 * 800 which is equal to 808.<BR>\n" );
document.write( "you pay 108 and the remaining balance is now 700.<BR>\n" );
document.write( "this continues until the end of the loan.\r<BR>\n" );
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document.write( "Based on these calculations, the total payments after 6 months is equal to 645 dollars.  \r<BR>\n" );
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document.write( "the actual sequence of payments is 110, 109, 108, 107, 106, 105, ...\r<BR>\n" );
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document.write( "the remaining balance after 6 months is equal to 400.  \r<BR>\n" );
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document.write( "the actual sequence of the remaining balance is 900, 800, 700, 600, 500, 400, ...\r<BR>\n" );
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document.write( "these are both arithmetic sequences.\r<BR>\n" );
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document.write( "the formula for the nth term of an arithmetic sequence is An = A1 + (n-1)d\r<BR>\n" );
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document.write( "for the payments, that formula becomes An = 110 + (n-1) * (-1)\r<BR>\n" );
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document.write( "for the remaining balance, that formula becomes An = 900 + (n-1) * (-100)\r<BR>\n" );
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document.write( "the sum of the elements in an arithmetic sequence is equal to n * (A1 + An) / 2\r<BR>\n" );
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document.write( "for the 6th month, the numbers become:\r<BR>\n" );
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document.write( "payments:\r<BR>\n" );
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document.write( "A6 = 110 + (5) * (-1) = 110 - 5 = 105\r<BR>\n" );
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document.write( "Sum(An) from n = 1 to 6 = 6 * (110 + 105) / 2 = 6 * 215 / 2 = 3 * 215 = 645.\r<BR>\n" );
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document.write( "remaining balance:\r<BR>\n" );
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document.write( "A6 = 900 + (5) * (-100) = 900 - 500 = 400\r<BR>\n" );
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document.write( "sum of remaining balance doesn't apply to the remaining balance.  \r<BR>\n" );
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document.write( "the payments and remaining balance for each time period of the loan are shown in the following picture of the excel spreadsheet used to make the calculations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/073002.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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