document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109670>Question 1109670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of terms in an A.P. whose first term is 5, common difference 3, and sum 55 is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724643 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for the sum of the first n terms of a arithmetic progression(AP) when we do not know the nth term is<BR>\n" );
document.write( ":<BR>\n" );
document.write( "s(n) = (n/2) * (2 * a(0) + (n-1) * d), where a(0) is the first term and d is the common difference <BR>\n" );
document.write( ":<BR>\n" );
document.write( "we are given<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(1) 55 = (n/2) * (2*5 + 3*(n-1)) <BR>\n" );
document.write( ":<BR>\n" );
document.write( "solve for n<BR>\n" );
document.write( ":<BR>\n" );
document.write( "55 = (n/2) * (10 + 3n - 3)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "110 = n * (7 + 3n)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "3n^2 +7n -110 = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(3n+22) * (n-5) = 0<BR>\n" );
document.write( ":<BR>\n" );
document.write( "n = -22/7 and n = 5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "we reject the negative value for n<BR>\n" );
document.write( ":<BR>\n" );
document.write( "****************************************<BR>\n" );
document.write( "there are 5 terms, namely<BR>\n" );
document.write( ":<BR>\n" );
document.write( "5, 8, 11, 14 , 17<BR>\n" );
document.write( ": <BR>\n" );
document.write( "to check this we use the formula<BR>\n" );
document.write( ":<BR>\n" );
document.write( "55 = (5/2) * (2 * 5 + 3 * (5 - 1)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "55 = (5/2) * 22 = 55<BR>\n" );
document.write( ":<BR>\n" );
document.write( "our answer checks<BR>\n" );
document.write( "*****************************************<BR>\n" );
document.write( ":<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );