document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110258>Question 1110258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The second, fourth and eight terms of an A.p from the first three consecutive terms of a G.P.  the sum of the third and fifth terms of the A.p is 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 #725278 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The second, fourth and eight terms of an A.p form the first three consecutive terms of a G.P.  the sum of the third and fifth terms of the A.p is 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.\r<BR>\n" );
document.write( "\n" );
document.write( "The second fourth and eighth terms can be written as<BR>\n" );
document.write( "a+d , a+3d,a+7d \r<BR>\n" );
document.write( "\n" );
document.write( "They are in GP\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B3d%29%2F%28a%2Bd%29+=+%28a%2B7d%29+%2F%28a%2B3d%29 ALIGN=MIDDLE  ALT=\"%28a%2B3d%29%2F%28a%2Bd%29+=+%28a%2B7d%29+%2F%28a%2B3d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B3d%29%5E2+=+%28a%2Bd%29%28a%2B7d%29 ALIGN=MIDDLE  ALT=\"%28a%2B3d%29%5E2+=+%28a%2Bd%29%28a%2B7d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+%2B6ad%2B9d%5E2+=a%5E2+%2B8ad+%2B7d%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+%2B6ad%2B9d%5E2+=a%5E2+%2B8ad+%2B7d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2ad+=+2d%5E2 ALIGN=MIDDLE  ALT=\"2ad+=+2d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "therefore a=d\r<BR>\n" );
document.write( "\n" );
document.write( "as per second condition and a=d<BR>\n" );
document.write( "a+2d +a+4d =20<BR>\n" );
document.write( "8d =20<BR>\n" );
document.write( "d=5/2  but d=a <BR>\n" );
document.write( "First four terms are\r<BR>\n" );
document.write( "\n" );
document.write( "t1=5/2<BR>\n" );
document.write( "t2=5/2 +5/2 = 5<BR>\n" );
document.write( "t3 = 5 + 5/2 = 15/2<BR>\n" );
document.write( "t4 = 15/2 + 5/2 = 10\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tn+=+%28n%2F2%29%28+2a%2B%28n-1%29d%29 ALIGN=MIDDLE  ALT=\"tn+=+%28n%2F2%29%28+2a%2B%28n-1%29d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S10+=+%2810%2F2%29%28+2%285%2F2%29+%2B+%2810-1%29%285%2F2%29%29 ALIGN=MIDDLE  ALT=\"S10+=+%2810%2F2%29%28+2%285%2F2%29+%2B+%2810-1%29%285%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "you can calculate S10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "t8 = a+7d = 5/2 + 7(5/2) = 20\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );