document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=85945>Question 85945</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tuition:  A student paid $6500 tuition for her first year attending a university. Tuition at the university is projected to increase $750 a year for the next four years.\r<BR>\n" );
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document.write( "(a)  	How much tuition should the student expect to pay for her fourth year at the university?\r<BR>\n" );
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document.write( "(b) 	How much should the student expect to pay in tuition for all four years?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #62105 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=62105\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First year tuition = $6500<BR>\n" );
document.write( "Second year tuition = $6500 + $750 = $7250<BR>\n" );
document.write( "Third year tuition = $7250 + $750 = $8000<BR>\n" );
document.write( "Fourth year tuition = $8000 + $750 = $8750<BR>\n" );
document.write( "Graduation<BR>\n" );
document.write( "(a) She should expect to pay $8750 for her fourth year tuition.<BR>\n" );
document.write( "(b) The total tuition she will pay is $6500 + $7250 + $8000 + 8750 = $30,500<BR>\n" );
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document.write( "You might notice that this is an arithmetic progression. The first term (call it \"a\") is<BR>\n" );
document.write( "$6500.  The common difference between terms (call it \"d\") is $750. The number of terms in<BR>\n" );
document.write( "the progression (call it \"n\") is 4, and the last term (call it \"L\") is 4.<BR>\n" );
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document.write( "The last term in an arithmetic progression is given by the equation:<BR>\n" );
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document.write( "L = a + (n-1)*d<BR>\n" );
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document.write( "Substitute the known values for a, n, and d to get:<BR>\n" );
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document.write( "L = $6500 + (4-1)*$750 = $6500 + 3*$750 = $6500 + $2250 = $8750<BR>\n" );
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document.write( "Notice that this is the answer to question (a) above.  She should expect to pay $8750 in<BR>\n" );
document.write( "tuition for her last year.<BR>\n" );
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document.write( "The sum (call it \"S\")of a finite number of terms in an arithmetic progression is given by <BR>\n" );
document.write( "the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+%28n%2A%282a+%2B+%28n-1%29%2Ad%29%29%2F2 ALIGN=MIDDLE  ALT=\"S+=+%28n%2A%282a+%2B+%28n-1%29%2Ad%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Substitute the values of a, d, and n for this problem and the sum becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%284%2A%28%282%2A6500%29%2B%284-1%29%2A750%29%29%2F2=%284%2A%2813000%2B3%2A%28750%29%29%29%2F2=%284%2A%2813000%2B2250%29%29%2F2=%284%2A15250%29%2F2+=+61000%2F2=30500 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So using the equation for the sum you can find the total paid for the four years of tuition<BR>\n" );
document.write( "is $30,500 ... the same as we calculated previously.<BR>\n" );
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document.write( "Hope this helps you to understand arithmetic progressions and the equations for finding the<BR>\n" );
document.write( "last term and the sum of the terms. </SPAN>\n" );
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