document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184673>Question 1184673</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question<BR>\n" );
document.write( "the fifth, ninth and sixteenth term of a linear sequence(a.p) are consecutive terms of an exponential sequence(g.p) <BR>\n" );
document.write( "(i) find the common difference of the linear sequence in terms of the first terms <BR>\n" );
document.write( "(ii) show that the twenty-first,thirty-seventh and sixty-fifth terms of the linear sequence are consecutive terms of an exponential sequence whose common ratio is 7/4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #815305 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=815305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(i) 5th term of the ap: a+4d<BR>\n" );
document.write( "9th term: a+8d<BR>\n" );
document.write( "16th term: a+15d<br><BR>\n" );
document.write( "In a gp, the square of any term is equal to the product of the terms before and after it:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B8d%29%5E2=%28a%2B4d%29%28a%2B15d%29 ALIGN=MIDDLE  ALT=\"%28a%2B8d%29%5E2=%28a%2B4d%29%28a%2B15d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B16ad%2B64d%5E2=a%5E2%2B19ad%2B60d%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B16ad%2B64d%5E2=a%5E2%2B19ad%2B60d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4d%5E2-3ad=0 ALIGN=MIDDLE  ALT=\"4d%5E2-3ad=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%284d-3a%29=0 ALIGN=MIDDLE  ALT=\"d%284d-3a%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The problem is of little interest if d=0, so<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4d-3a=0 ALIGN=MIDDLE  ALT=\"4d-3a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4d=3a ALIGN=MIDDLE  ALT=\"4d=3a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%283%2F4%29a ALIGN=MIDDLE  ALT=\"d=%283%2F4%29a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "(i) ANSWER: d = (3/4)a<br><BR>\n" );
document.write( "(ii) 21st term: a+20d = a+15a = 16a<BR>\n" );
document.write( "37th term: a+36d = a+27a = 28a<BR>\n" );
document.write( "65th term: a+64d = a+48a = 49a<br><BR>\n" );
document.write( "28a/16a = 7/4; 49a/28a = 7/4; this sequence is geometric with common ratio 7/4<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );