document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209188>Question 1209188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first and last terms of an A.P are 1 and 121 respectively. Find <BR>\n" );
document.write( "(a) the number of terms in the A.P<BR>\n" );
document.write( "(b) the commons difference if the sum of its term is 671 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847789 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "n = number of terms<BR>\n" );
document.write( "d = common difference<BR>\n" );
document.write( "a<sub>1</sub> = first term = 1<BR>\n" );
document.write( "a<sub>n</sub> = n<sup>th</sup> term = 121\r<BR>\n" );
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document.write( "S<sub>n</sub> = sum of the first n terms of an arithmetic sequence<BR>\n" );
document.write( "S<sub>n</sub> = (n/2)*(a<sub>1</sub>+a<sub>n</sub>)<BR>\n" );
document.write( "671 = (n/2)*(1+121)<BR>\n" );
document.write( "671 = (n/2)*122<BR>\n" );
document.write( "671 = 61n<BR>\n" );
document.write( "n = 671/61<BR>\n" );
document.write( "<font color=red>n = 11</font><BR>\n" );
document.write( "There are <font color=red>11 terms</font> in this arithmetic sequence.\r<BR>\n" );
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document.write( "a<sub>n</sub> = n<sup>th</sup> term <BR>\n" );
document.write( "a<sub>n</sub> = a<sub>1</sub> + d*(n-1)<BR>\n" );
document.write( "a<sub>11</sub> = 1 + d*(11-1)<BR>\n" );
document.write( "121 = 1 + d*(11-1)<BR>\n" );
document.write( "121 = 1 + 10d<BR>\n" );
document.write( "10d = 121-1<BR>\n" );
document.write( "10d = 120<BR>\n" );
document.write( "d = 120/10<BR>\n" );
document.write( "<font color=red>d = 12<BR>\n" );
document.write( "The common difference is 12</font>.\r<BR>\n" );
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document.write( "The arithmetic sequence is: 1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121<BR>\n" );
document.write( "I used GeoGebra to generate the sequence quickly. You can also use a spreadsheet to generate the list.<BR>\n" );
document.write( "The sum of these values is 671 to help confirm the answers are correct.<BR>\n" );
document.write( "I don't recommend manually typing 1+13+25+37+49+61+73+85+97+109+121 into a calculator such as a TI83 since it would be tedious busy-work.\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "(a) <font color=red>11 terms</font><BR>\n" );
document.write( "(b) <font color=red>common difference is 12</font><BR>\n" );
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