document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969971>Question 969971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem<BR>\n" );
document.write( "the sequence is as follows<BR>\n" );
document.write( "-----  , 3 , 17<BR>\n" );
document.write( "What is the first term?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592668 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=592668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We need more information than that.<BR>\n" );
document.write( "Is there a commonly used pattern to your sequence?<BR>\n" );
document.write( "Is 3 the second term, and 17 the third term?<BR>\n" );
document.write( " <BR>\n" );
document.write( "A sequence could have no rhyme or reason, such as<BR>\n" );
document.write( "potato , 3 , 7, duck , 1 , chair .<BR>\n" );
document.write( "However, in algebra class teachers like sequences made with some sort of pattern.<BR>\n" );
document.write( "The sequences with the commonly used patterns are an arithmetic sequence or a geometric sequence.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If it is an arithmetic sequence, then each term is the one before plus a fixed number, <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( "That number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > is called the common difference, because it is the difference between any two consecutive terms.<BR>\n" );
document.write( "So, term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "is related to the previous term,<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;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D=a%5Bn%5D%2Bd ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D=a%5Bn%5D%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=a%5Bn%2B1%5D-a%5Bn%5D ALIGN=MIDDLE  ALT=\"d=a%5Bn%2B1%5D-a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for all natural number (counting number) values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If 3 and 17 are the 2nd and 3rd terms respectively,<BR>\n" );
document.write( "then the common difference between consecutive terms is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d-17-3=14 ALIGN=MIDDLE  ALT=\"d-17-3=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Each term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14 ALIGN=MIDDLE  ALT=\"14\"   DISABLED_style= \"max-width:90%; height:auto;\" > more than the one before.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=3 ALIGN=MIDDLE  ALT=\"a%5B2%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B3%5D=17 ALIGN=MIDDLE  ALT=\"a%5B3%5D=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=14 ALIGN=MIDDLE  ALT=\"d=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the first term that we want to find.<BR>\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%2B1%5D=a%5Bn%5D%2Bd ALIGN=MIDDLE  ALT=\"a%5Bn%2B1%5D=a%5Bn%5D%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" > , for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%2B1%5D=a%5B1%5D%2Bd ALIGN=MIDDLE  ALT=\"a%5B1%2B1%5D=a%5B1%5D%2Bd\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D=a%5B1%5D%2B14 ALIGN=MIDDLE  ALT=\"a%5B2%5D=a%5B1%5D%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=a%5B1%5D%2B14 ALIGN=MIDDLE  ALT=\"3=a%5B1%5D%2B14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D%2B14=3 ALIGN=MIDDLE  ALT=\"a%5B1%5D%2B14=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=3-14 ALIGN=MIDDLE  ALT=\"a%5B1%5D=3-14\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D=-11 ALIGN=MIDDLE  ALT=\"a%5B1%5D=-11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If it is a geometric sequence, then each term is the one before times a fixed number, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is called the common ratio, because it is the ratio between any two consecutive terms.<BR>\n" );
document.write( "So, term number <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2B1 ALIGN=MIDDLE  ALT=\"n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%2B1%5D ALIGN=MIDDLE  ALT=\"b%5Bn%2B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "is related to the previous term,<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;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%5D ALIGN=MIDDLE  ALT=\"b%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%2B1%5D=b%5Bn%5D%2Ar ALIGN=MIDDLE  ALT=\"b%5Bn%2B1%5D=b%5Bn%5D%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=b%5Bn%2B1%5D%2Fb%5Bn%5D ALIGN=MIDDLE  ALT=\"r=b%5Bn%2B1%5D%2Fb%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "for all natural number (counting number) values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n ALIGN=MIDDLE  ALT=\"n\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If 3 and 17 are the 2nd and 3rd terms respectively,<BR>\n" );
document.write( "then the common ratio between consecutive terms is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=17%2F3 ALIGN=MIDDLE  ALT=\"r=17%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Each term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17%2F3 ALIGN=MIDDLE  ALT=\"17%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the one before.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B2%5D=3 ALIGN=MIDDLE  ALT=\"b%5B2%5D=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B3%5D=17 ALIGN=MIDDLE  ALT=\"b%5B3%5D=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=17%2F3 ALIGN=MIDDLE  ALT=\"r=17%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D ALIGN=MIDDLE  ALT=\"b%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the first term that we want to find.<BR>\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5Bn%2B1%5D=b%5Bn%5D%2Ar ALIGN=MIDDLE  ALT=\"b%5Bn%2B1%5D=b%5Bn%5D%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" > , for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1 ALIGN=MIDDLE  ALT=\"n=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%2B1%5D=b%5B1%5D%2Ar ALIGN=MIDDLE  ALT=\"b%5B1%2B1%5D=b%5B1%5D%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B2%5D=b%5B1%5D%2817%2F3%29 ALIGN=MIDDLE  ALT=\"b%5B2%5D=b%5B1%5D%2817%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=b%5B1%5D%2817%2F3%29 ALIGN=MIDDLE  ALT=\"3=b%5B1%5D%2817%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so ---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D%2817%2F3%29=3 ALIGN=MIDDLE  ALT=\"b%5B1%5D%2817%2F3%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D=3%2F%28%2817%2F3%29%29 ALIGN=MIDDLE  ALT=\"b%5B1%5D=3%2F%28%2817%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D=3%283%2F17%29 ALIGN=MIDDLE  ALT=\"b%5B1%5D=3%283%2F17%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5B1%5D=9%2F17 ALIGN=MIDDLE  ALT=\"b%5B1%5D=9%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );