document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=622864>Question 622864</A>: <I><SPAN STYLE=\"word-break: break-all;\"> First Question:  Find the initial term of the arithmetic sequence with 10th term -1 and 20th term 7. (use initial term a0)\r<BR>\n" );
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document.write( "Second Question: There are two geometric sequences with 2nd term 5 and 4th term 80.  What are the two possible values of the 3rd term?\r<BR>\n" );
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document.write( "I truly appreciate 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 #391699 by </B><A HREF=/tutors/aboutme.mpl?userid=MathTherapy><B>MathTherapy(10552)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathTherapy><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=MathTherapy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=391699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Using the formula for an arithmetic sequence<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bn%5D+=+t%5B1%5D+%2B+%28n+-+1%29d ALIGN=MIDDLE  ALT=\"t%5Bn%5D+=+t%5B1%5D+%2B+%28n+-+1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B10%5D+=+t%5B1%5D+%2B+%28n+-+1%29d ALIGN=MIDDLE  ALT=\"t%5B10%5D+=+t%5B1%5D+%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=t%5B10%5D+=+t%5B1%5D+%2B+%2810+-+1%29d ALIGN=MIDDLE  ALT=\"t%5B10%5D+=+t%5B1%5D+%2B+%2810+-+1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Substituting 10 for n in formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+1+=+t%5B1%5D+%2B+%2810+-+1%29d ALIGN=MIDDLE  ALT=\"-+1+=+t%5B1%5D+%2B+%2810+-+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=-+1+=+t%5B1%5D+%2B+9d ALIGN=MIDDLE  ALT=\"-+1+=+t%5B1%5D+%2B+9d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+%2B+9d+=+-+1 ALIGN=MIDDLE  ALT=\"t%5B1%5D+%2B+9d+=+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- eq (i)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bn%5D+=+t%5B1%5D+%2B+%28n+-+1%29d ALIGN=MIDDLE  ALT=\"t%5Bn%5D+=+t%5B1%5D+%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=t%5B20%5D+=+t%5B1%5D+%2B+%2820+-+1%29d ALIGN=MIDDLE  ALT=\"t%5B20%5D+=+t%5B1%5D+%2B+%2820+-+1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Substituting 20 for n in formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+=+t%5B1%5D+%2B+%2820+-+1%29d ALIGN=MIDDLE  ALT=\"7+=+t%5B1%5D+%2B+%2820+-+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=7+=+t%5B1%5D+%2B+19d ALIGN=MIDDLE  ALT=\"7+=+t%5B1%5D+%2B+19d\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+%2B+19d+=+7 ALIGN=MIDDLE  ALT=\"t%5B1%5D+%2B+19d+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ------ eq (ii)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+%2B+9d+=+-+1 ALIGN=MIDDLE  ALT=\"t%5B1%5D+%2B+9d+=+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- eq (i)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+%2B+19d+=+7 ALIGN=MIDDLE  ALT=\"t%5B1%5D+%2B+19d+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- eq (ii) <BR>\n" );
document.write( "- 10d = - 8 ------ Subtracting eq (ii) from eq (i)<BR>\n" );
document.write( "d, or difference = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-+8%29%2F-+10 ALIGN=MIDDLE  ALT=\"%28-+8%29%2F-+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bn%5D+=+t%5B1%5D+%2B+%28n+-+1%29d ALIGN=MIDDLE  ALT=\"t%5Bn%5D+=+t%5B1%5D+%2B+%28n+-+1%29d\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B10%5D+=+t%5B1%5D+%2B+%2810+-+1%29+%2A+%284%2F5%29 ALIGN=MIDDLE  ALT=\"t%5B10%5D+=+t%5B1%5D+%2B+%2810+-+1%29+%2A+%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ----- Substituting 10 for n, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F5 ALIGN=MIDDLE  ALT=\"4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > for d in formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+1+=+t%5B1%5D+%2B+9+%2A+%284%2F5%29 ALIGN=MIDDLE  ALT=\"-+1+=+t%5B1%5D+%2B+9+%2A+%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+1+=+t%5B1%5D+%2B+%2836%2F5%29 ALIGN=MIDDLE  ALT=\"-+1+=+t%5B1%5D+%2B+%2836%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+-+1+-+%2836%2F5+%29 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+-+1+-+%2836%2F5+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+-+%285%2F5%29+-+%2836%2F5%29 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+-+%285%2F5%29+-+%2836%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Initial term, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28t%5B1%5D+=+-+%2841%2F5%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28t%5B1%5D+=+-+%2841%2F5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=========<BR>\n" );
document.write( "Check<BR>\n" );
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document.write( "10th term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Bn%5D+=+t%5B1%5D+%2B+%28n+-+1%29d ALIGN=MIDDLE  ALT=\"t%5Bn%5D+=+t%5B1%5D+%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=-+1+=+%28-+41%2F5%29+%2B+%2810+-+1%29+%2A+%284%2F5%29 ALIGN=MIDDLE  ALT=\"-+1+=+%28-+41%2F5%29+%2B+%2810+-+1%29+%2A+%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+1+=+%28-+41%2F5%29+%2B+9+%2A+%284%2F5%29 ALIGN=MIDDLE  ALT=\"-+1+=+%28-+41%2F5%29+%2B+9+%2A+%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+1+=+%28-+41%2F5%29+%2B+%2836%2F5%29 ALIGN=MIDDLE  ALT=\"-+1+=+%28-+41%2F5%29+%2B+%2836%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+1+=+-+%285%2F5%29 ALIGN=MIDDLE  ALT=\"-+1+=+-+%285%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "- 1 = - 1 (TRUE)\r<BR>\n" );
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document.write( "20th term<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+=+%28-+41%2F5%29+%2B+%2820+-+1%29+%2A+%284%2F5%29 ALIGN=MIDDLE  ALT=\"7+=+%28-+41%2F5%29+%2B+%2820+-+1%29+%2A+%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+=+%28-+41%2F5%29+%2B+19+%2A+%284%2F5%29 ALIGN=MIDDLE  ALT=\"7+=+%28-+41%2F5%29+%2B+19+%2A+%284%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+=+%28-+41%2F5%29+%2B+%2876%2F5%29 ALIGN=MIDDLE  ALT=\"7+=+%28-+41%2F5%29+%2B+%2876%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+=+%2835%2F5%29 ALIGN=MIDDLE  ALT=\"7+=+%2835%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "7 = 7 (TRUE)\r<BR>\n" );
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document.write( "Send comments and “thank-yous” to “D” at  MathMadEzy@aol.com </SPAN>\n" );
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