document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110298>Question 1110298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The second, fourth and eight terms of an A.p<BR>\n" );
document.write( "form the first three consecutive terms of a G.P.<BR>\n" );
document.write( "the sum of the third and fifth terms of the A.p is<BR>\n" );
document.write( "equal to 20. Find the (a) first 4 terms of the A.p<BR>\n" );
document.write( "(b) sum of the first 10 terms of the A.p. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725300 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=725300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Since the sum of the 3rd and 5th terms of the AP is 20, the 4th term is 10.<br><BR>\n" );
document.write( "If the common difference in the AP is d, then the 2nd term is 10-2d and the 8th term is 10+4d.  Since the 2nd, 4th, and 8th terms of the AP form a GP,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2F%2810-2d%29+=+%2810%2B4d%29%2F10 ALIGN=MIDDLE  ALT=\"10%2F%2810-2d%29+=+%2810%2B4d%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2B20d-8d%5E2+=+100 ALIGN=MIDDLE  ALT=\"100%2B20d-8d%5E2+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20d-8d%5E2+=+0 ALIGN=MIDDLE  ALT=\"20d-8d%5E2+=+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%285-2d%29+=+0 ALIGN=MIDDLE  ALT=\"4d%285-2d%29+=+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+=+0 ALIGN=MIDDLE  ALT=\"d+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+2.5 ALIGN=MIDDLE  ALT=\"d+=+2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Both values of d satisfy the conditions of the problem; but the AP with d=0 is not very interesting.<br><BR>\n" );
document.write( "With d=2.5 and the 4th term=10, the AP is<BR>\n" );
document.write( "2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25, ...<br><BR>\n" );
document.write( "Answers:<BR>\n" );
document.write( "a) 2.5, 5, 7.5, 10<BR>\n" );
document.write( "b) (number of terms) times (average of first and last terms) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%28%282.5%2B25%29%2F2%29+=+5%2A27.5+=+137.5 ALIGN=MIDDLE  ALT=\"10%28%282.5%2B25%29%2F2%29+=+5%2A27.5+=+137.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );