document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209375>Question 1209375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let a_1, a_2, a_3, ..., a_8, a_9, a_{10} be an arithmetic sequence.  If a_1 + a_3 + a_5 = 5 and a_2 + a_4 = -2, then find a_1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848706 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=848706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I agree with the other tutor. The way this problem is set up leads to a contradiction.<BR>\n" );
document.write( "a<sub>1</sub>+a<sub>3</sub>+a<sub>5</sub> = 5<BR>\n" );
document.write( "a<sub>2</sub>+a<sub>4</sub> = -2\r<BR>\n" );
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document.write( "Add the equations to arrive at<BR>\n" );
document.write( "a<sub>1</sub>+a<sub>2</sub>+a<sub>3</sub>+a<sub>4</sub>+a<sub>5</sub> = 3<BR>\n" );
document.write( "which means<BR>\n" );
document.write( "S<sub>5</sub> = 3\r<BR>\n" );
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document.write( "S<sub>5</sub> represents the sum of the first 5 terms of the arithmetic sequence.\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( "S<sub>5</sub> = (5/2)*(a<sub>1</sub> + a<sub>5</sub>)<BR>\n" );
document.write( "3 = 2.5*(a<sub>1</sub> + a<sub>5</sub>)<BR>\n" );
document.write( "a<sub>1</sub> + a<sub>5</sub> = 3/(2.5)<BR>\n" );
document.write( "a<sub>1</sub> + a<sub>5</sub> = 1.2\r<BR>\n" );
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document.write( "a<sub>1</sub>+a<sub>3</sub>+a<sub>5</sub> = 5<BR>\n" );
document.write( "(a<sub>1</sub>+a<sub>5</sub>)+a<sub>3</sub> = 5<BR>\n" );
document.write( "1.2+a<sub>3</sub> = 5<BR>\n" );
document.write( "a<sub>3</sub> = 5-1.2<BR>\n" );
document.write( "<font color=blue>a<sub>3</sub> = 3.8</font>\r<BR>\n" );
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document.write( "Then consider:<BR>\n" );
document.write( "a<sub>2</sub>+a<sub>4</sub> = -2<BR>\n" );
document.write( "(a<sub>3</sub>-d)+(a<sub>3</sub>+d) = -2<BR>\n" );
document.write( "2*a<sub>3</sub> = -2<BR>\n" );
document.write( "a<sub>3</sub> = -2/2<BR>\n" );
document.write( "<font color=red>a<sub>3</sub> = -1</font>\r<BR>\n" );
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document.write( "But this contradicts <font color=blue>a<sub>3</sub> = 3.8</font> found in the previous section.<BR>\n" );
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