document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60451>Question 60451</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi, I'm Sarah and i'm in 10th grade taking algebra 2, but i'm also taking an SAT prep course, and i'm having a little trouble with questions involving finding the nth term. it's quite a bit more advanced than regular math, but i hope you can still give me a hand. here is an example of one of the problems i was given:\r<BR>\n" );
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document.write( "Instructions: writs the general term of the sequence:<BR>\n" );
document.write( "1,8,27,64,125,...  \r<BR>\n" );
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document.write( "(answer goes here) -> Nth term: \r<BR>\n" );
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document.write( "i was also given problems using variables; but i can't understand them without first understanding how to find the answer using numerical values. i would be most appreciative if you could also work one of the questions with variables so i can get an idea of how to work them. here is a question with variables:\r<BR>\n" );
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document.write( "The sequence a, a+d, a+2d, a+3d, a+4d,... has as it's Nth or general term (answer goes in blank) -> _________\r<BR>\n" );
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document.write( "thank you in advance for your help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41522 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=41522\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at the numbers in terms of what powers they are of what numbers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2+=+4 ALIGN=MIDDLE  ALT=\"2%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E3+=+8 ALIGN=MIDDLE  ALT=\"2%5E3+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E4+=+16 ALIGN=MIDDLE  ALT=\"2%5E4+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" > etc.<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2+=+9 ALIGN=MIDDLE  ALT=\"3%5E2+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E3+=+27 ALIGN=MIDDLE  ALT=\"3%5E3+=+27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E4+=+81 ALIGN=MIDDLE  ALT=\"3%5E4+=+81\"   DISABLED_style= \"max-width:90%; height:auto;\" > etc.<BR>\n" );
document.write( "look at your sequence number by number<BR>\n" );
document.write( "1,8,27,64,125<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+1%5E2 ALIGN=MIDDLE  ALT=\"1+=+1%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8+=+2%5E3 ALIGN=MIDDLE  ALT=\"8+=+2%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27+=+3%5E3 ALIGN=MIDDLE  ALT=\"27+=+3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64+=+4%5E3 ALIGN=MIDDLE  ALT=\"64+=+4%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=125+=+5%5E3 ALIGN=MIDDLE  ALT=\"125+=+5%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first one is out of place but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E2+=+1 ALIGN=MIDDLE  ALT=\"1%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%5E3+=+1 ALIGN=MIDDLE  ALT=\"1%5E3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > also<BR>\n" );
document.write( "so, the sequence is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E3 ALIGN=MIDDLE  ALT=\"n%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where n is the position in the sequence.<BR>\n" );
document.write( "Test yourself. What is the 11th term?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1331+=+11%5E3 ALIGN=MIDDLE  ALT=\"1331+=+11%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "what is the 10,000th term?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E12+=+10000%5E3 ALIGN=MIDDLE  ALT=\"10%5E12+=+10000%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------<BR>\n" );
document.write( " a, a+d, a+2d, a+3d, a+4d,...<BR>\n" );
document.write( "a is the same in each term so, it's a + something<BR>\n" );
document.write( "The multiplier for d looks like its position in the series minus one<BR>\n" );
document.write( "n = position<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+%28n-1%29d ALIGN=MIDDLE  ALT=\"a+%2B+%28n-1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "test this to see if it works for each term<BR>\n" );
document.write( "1st term: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+%281-1%29d+=+a ALIGN=MIDDLE  ALT=\"a+%2B+%281-1%29d+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2nd term: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+%282-1%29d+=+a+%2B+d ALIGN=MIDDLE  ALT=\"a+%2B+%282-1%29d+=+a+%2B+d\"   DISABLED_style= \"max-width:90%; height:auto;\" > etc.<BR>\n" );
document.write( "  </SPAN>\n" );
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