document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012889>Question 1012889</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find five consecutive terms of an arithmetic progression whose sum is 115 and sum of squares of its second and fourth term is 1156. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #629004 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=629004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The five terms are a, a+d, a+2d, a+3d and a+4d.<BR>\n" );
document.write( "If we add them we get<BR>\n" );
document.write( "5a + 10d = 115  or<BR>\n" );
document.write( "a + 2d = 23 or<BR>\n" );
document.write( "a = 23 - 2d<BR>\n" );
document.write( "We also have<BR>\n" );
document.write( "(a+d)^2 + (a+3d)^2 = 1156<BR>\n" );
document.write( "We can substitute from before into this and get<BR>\n" );
document.write( "(23 - 2d + d)^2 + (23 - 2d + 3d)^2 = 1156<BR>\n" );
document.write( "(23 - d)^2 + (23 + d)^2 = 1156<BR>\n" );
document.write( "529 - 46d + d^2 + 529 + 46d + d^2 = 1156<BR>\n" );
document.write( "2d^2 + 1058 = 1156<BR>\n" );
document.write( "2d^2 = 98<BR>\n" );
document.write( "d^2 = 49<BR>\n" );
document.write( "d = 7, -7<BR>\n" );
document.write( "a is then 23 - 2(7) = 9 or 23 - 2(-7) = 37<BR>\n" );
document.write( "Thus our two possibilities appear to be<BR>\n" );
document.write( "9, 16, 23, 30, 37  and<BR>\n" );
document.write( "37, 30, 23, 16, 9\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );