document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175215>Question 175215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I solve this problem? the first two terms of an arithmetic sequence are a(base1)=2 and a(base2)=4. what is the a(base10)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130312 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=130312\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for the nth term of a geometric sequence is:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "you are given <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;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "you use them to find r as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+a%5B1%5D%2Ar%5E%282-1%29 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a%5B1%5D%2Ar%5E%282-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+a%5B1%5D%2Ar%5E1 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a%5B1%5D%2Ar%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substituting 4 for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 2 for <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;\" > you get:<BR>\n" );
document.write( "4 = 2*r^1 = 2*r<BR>\n" );
document.write( "solving for r, you get<BR>\n" );
document.write( "r = 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "you now have r, and you can substitute in the general equation as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+a%5B1%5D%2Ar%5E%28n-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substitute 2 for r, and 2 for <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;\" > and you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D+=+2%2A2%5E%2810-1%29 ALIGN=MIDDLE  ALT=\"a%5Bn%5D+=+2%2A2%5E%2810-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2*2^9 = 2*512 = 1024.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the 10th term in the sequence is 1024.<BR>\n" );
document.write( "you can test this by doing it the hard way (each term is done separately) as follows:<BR>\n" );
document.write( "a(1) = 2<BR>\n" );
document.write( "a(2) = 4<BR>\n" );
document.write( "a(3) = 8<BR>\n" );
document.write( "a(4) = 16<BR>\n" );
document.write( "a(5) = 32<BR>\n" );
document.write( "a(6) = 64<BR>\n" );
document.write( "a(7) = 128<BR>\n" );
document.write( "a(8) = 256<BR>\n" );
document.write( "a(9) = 512<BR>\n" );
document.write( "a(10) = 1024<BR>\n" );
document.write( "---<BR>\n" );
document.write( "each succeeding number is multiplied by the ratio.<BR>\n" );
document.write( "you do that 9 times which is the same as multiplying the original number by 2^9.<BR>\n" );
document.write( " </SPAN>\n" );
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