document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662461>Question 662461</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question: In an arithmetic series of 50 terms, the 17th term is 53 and the 28th term is 86. Find the sum of the series.\r<BR>\n" );
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document.write( "Problem: I've gone through all the steps but I ended up with a different answer than what's in the back of my textbook. I'm going to type everything thing I did below, and hopefully someone can tell me where I messed up. I used \ when referring to division and / when referring to a fraction.\r<BR>\n" );
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document.write( "t17=53<BR>\n" );
document.write( "t28=86\r<BR>\n" );
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document.write( "tn=a+(n-1)d<BR>\n" );
document.write( "53=a+(17-1)d<BR>\n" );
document.write( "53=a+16d<BR>\n" );
document.write( "a=53-16d\r<BR>\n" );
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document.write( "Sn=n\2(2a+(n-1)d)<BR>\n" );
document.write( "86=28/2(2a+(28-1)d)<BR>\n" );
document.write( "86=14(2a+27d)\r<BR>\n" );
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document.write( "86=14(2(53-16d)+27d)<BR>\n" );
document.write( "6/1/7=2(53-16d)+27d<BR>\n" );
document.write( "6/1/7=106-32d+27d<BR>\n" );
document.write( "-99/6/7=5d<BR>\n" );
document.write( "-19/34/35=d\r<BR>\n" );
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document.write( "a=53-16(-19/34/35)<BR>\n" );
document.write( "a=53-320<BR>\n" );
document.write( "a=-267\r<BR>\n" );
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document.write( "Sn=n\2(2a+(n-1)d)<BR>\n" );
document.write( "Sn= 50\2(2(-267)+(50-1)-19/34/35)<BR>\n" );
document.write( "Sn=25(-534+(49)-19/34/34)<BR>\n" );
document.write( "Sn=25(-1512/3/5)<BR>\n" );
document.write( "Sn=-37815\r<BR>\n" );
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document.write( "The answer im the back of my textbook says it's suppose to be 3925 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412289 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=412289\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first part of your work is right.<BR>\n" );
document.write( "term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17 ALIGN=MIDDLE  ALT=\"17\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53 ALIGN=MIDDLE  ALT=\"53\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B17%5D=53 ALIGN=MIDDLE  ALT=\"t%5B17%5D=53\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bn%5D=a%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"t%5Bn%5D=a%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53=a%2B%2817-1%29d ALIGN=MIDDLE  ALT=\"53=a%2B%2817-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53=a%2B16d ALIGN=MIDDLE  ALT=\"53=a%2B16d\"   DISABLED_style= \"max-width:90%; height:auto;\" > <--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=53-16d ALIGN=MIDDLE  ALT=\"a=53-16d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You were on your way to finding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You just needed to use more data to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Next, you misinterpreted \"the 28th term is 86\" (or maybe lost track of your planned steps)<BR>\n" );
document.write( "You wrote <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=%28n%5C2%29%282a%2B%28n-1%29d%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=%28n%5C2%29%282a%2B%28n-1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the formula for sum of the first <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms,<BR>\n" );
document.write( "followed by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=86=%2828%2F2%29%282a%2B%2828-1%29d%29 ALIGN=MIDDLE  ALT=\"86=%2828%2F2%29%282a%2B%2828-1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as if the sum of the first 28 terms was 86.<BR>\n" );
document.write( "You knew that the next step would require using that formula for the sum,<BR>\n" );
document.write( "but lost track, and skipped a step.<BR>\n" );
document.write( " <BR>\n" );
document.write( "At that point, a bunch of people would write some of this:<BR>\n" );
document.write( "term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=86 ALIGN=MIDDLE  ALT=\"86\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B28%5D=86 ALIGN=MIDDLE  ALT=\"t%5B28%5D=86\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bn%5D=a%2B%28n-1%29d ALIGN=MIDDLE  ALT=\"t%5Bn%5D=a%2B%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=86=a%2B%2828-1%29d ALIGN=MIDDLE  ALT=\"86=a%2B%2828-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >  --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=86=a%2B27d ALIGN=MIDDLE  ALT=\"86=a%2B27d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, they would use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=86=a%2B27d ALIGN=MIDDLE  ALT=\"86=a%2B27d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, along with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=53=a%2B16d ALIGN=MIDDLE  ALT=\"53=a%2B16d\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "They would write the system <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2886=a%2B27d%2C53=a%2B16d%29 ALIGN=MIDDLE  ALT=\"system%2886=a%2B27d%2C53=a%2B16d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and would solve it to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=5%29 ALIGN=MIDDLE  ALT=\"highlight%28a=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=3%29 ALIGN=MIDDLE  ALT=\"highlight%28d=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "RANT:<BR>\n" );
document.write( "I may write all that to go with the flow, and please a teacher,<BR>\n" );
document.write( "but I prefer to use definitions, logic and 5th grader reasoning (if possible),<BR>\n" );
document.write( "trying to always understand the meaning of my calculations,<BR>\n" );
document.write( "rather than using formulas.<BR>\n" );
document.write( "I look at it the fifth grader way:<BR>\n" );
document.write( "Going from the 17th to the 28th term, we are adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > from one term to the next,<BR>\n" );
document.write( "and we do that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28-17=11 ALIGN=MIDDLE  ALT=\"28-17=11\"   DISABLED_style= \"max-width:90%; height:auto;\" > times,<BR>\n" );
document.write( "so the difference between the 17th and the 28th terms must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" > times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=86-53=33 ALIGN=MIDDLE  ALT=\"86-53=33\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so I divide to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=33%2F11=highlight%283%29 ALIGN=MIDDLE  ALT=\"d=33%2F11=highlight%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, since you gave me <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=53-16d ALIGN=MIDDLE  ALT=\"a=53-16d\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "I use it to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=53-16%2A3 ALIGN=MIDDLE  ALT=\"a=53-16%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=53-48 ALIGN=MIDDLE  ALT=\"a=53-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a=5%29 ALIGN=MIDDLE  ALT=\"highlight%28a=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "THE SUM:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=%28n%5C2%29%282a%2B%28n-1%29d%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=%28n%5C2%29%282a%2B%28n-1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B50%5D=%2850%5C2%29%282%2A5%2B%2850-1%29%2A3%29 ALIGN=MIDDLE  ALT=\"S%5B50%5D=%2850%5C2%29%282%2A5%2B%2850-1%29%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B50%5D=%2850%5C2%29%2810%2B49%2A3%29 ALIGN=MIDDLE  ALT=\"S%5B50%5D=%2850%5C2%29%2810%2B49%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B50%5D=%2850%5C2%29%2810%2B147%29 ALIGN=MIDDLE  ALT=\"S%5B50%5D=%2850%5C2%29%2810%2B147%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B50%5D=%2850%5C2%29%28157%29 ALIGN=MIDDLE  ALT=\"S%5B50%5D=%2850%5C2%29%28157%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28S%5B50%5D=3925%29 ALIGN=MIDDLE  ALT=\"highlight%28S%5B50%5D=3925%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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