document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191984>Question 1191984</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) The first term of an arithmetic progression is 7 and the common difference is 2. Find the 15th term and the sum of the first 15th term.<BR>\n" );
document.write( "(b) how many terms of the sequence -9,-6,-3 must be taken that the sum maybe 66.<BR>\n" );
document.write( "(c) find the sum of the first 25 even integers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823879 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sum=(n/2)(2a+(n-1)d)<BR>\n" );
document.write( "nth term =a1+(n-1)d<BR>\n" );
document.write( "a. n15=7+(15-1)2=35<BR>\n" );
document.write( "Sum is (15/2)(14+14*2)=315<BR>\n" );
document.write( "7+9+11+13+15+17+19+21+23+25+27+29+31+33+35=315<BR>\n" );
document.write( "-<BR>\n" );
document.write( "a1=-9, d=3, sum=66<BR>\n" );
document.write( "66=(n/2)(-18+(n-1)3)=(n/2)(-18+3n-3)=(n/2)(3n-21)<BR>\n" );
document.write( "multiply by 2 to clear fractions<BR>\n" );
document.write( "132=3n^2-21n<BR>\n" );
document.write( "n^2-7n-44=0 dividing by 3 and rearranging.<BR>\n" );
document.write( "(n-11)(n+4)=0<BR>\n" );
document.write( "n=11 terms only positive root.<BR>\n" );
document.write( "-9,-6,-3,0,3,6,9,12,15,18,21<BR>\n" );
document.write( "-<BR>\n" );
document.write( "This is n(n+1) where n=25<BR>\n" );
document.write( "The answer is 650.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );