document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=600581>Question 600581</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sum of Arithmetic sequence 1,-1,-3...-13\r<BR>\n" );
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document.write( "Find missing term in arithmetic sequence -17, a2, a3, 1 \r<BR>\n" );
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document.write( "Find missing term in arithmetic sequence 1, a2, a3, a4, -35 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379385 by </B><A HREF=/tutors/aboutme.mpl?userid=Nihal@SriLanka><B>Nihal@SriLanka(22)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Nihal@SriLanka><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=379385\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The nth term of an arithmetic sequence is given by the formula a+(n-1)d and the sum of the first n terms of an arithmetic sequence is given by the formula.\r<BR>\n" );
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document.write( "n/2 * (2a+(n-1)d) where a is the first term and d is the common difference\r<BR>\n" );
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document.write( "Substituting 1 for a and -2 for d in the first equation the nth term of the given sequence works out to 1+(n-1)(-2), i.e. 3-2n\r<BR>\n" );
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document.write( "Since -13 is the term up to which sum of terms is required we use the equation 3-2n=-13 to give us the value of n for which the term is of value -13.<BR>\n" );
document.write( "3-2n=-13 implies n=8 which means that n=8, i.e. -13 is the 8th term in the sequence.\r<BR>\n" );
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document.write( "Using the same values of a and d and n=8 in the formula for sum of n terms we end up with \r<BR>\n" );
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document.write( "8/2 * (2+(8-1)(-2)) = 8 * (1-8+1) = 8 * (-6) = -48 as the required sum.  \r<BR>\n" );
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document.write( "(also note sum of n terms for this particular sequence is given by the formula n/2 (2+(n-1)(-2))<BR>\n" );
document.write( "i.e. n((1-(n-1))<BR>\n" );
document.write( "i.e. n(1-n+1)<BR>\n" );
document.write( "i.e. n(2-n). Substituting 8 for n gives the answer as -48)\r<BR>\n" );
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document.write( "In the sequence -17, a2, a3, 1 a=-17 4th term= a+(4-1)d= -17 + 3d = 1 which implies d = 6. therefore a2 = -17 + 6 = -11 and a3 = a2 + 6 = -11 + 6 = -5. \r<BR>\n" );
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document.write( "Similarly in the sequence 1, a2, a3, a4, -35 a=1 5th term = a + (5-1)d = 1 + 4d = -35 which implies d=-9 and therefore a2 = 1-9 =-8, a3 = -8-9 = -17 and a4 = -17-9 = -26.\r<BR>\n" );
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document.write( "(if one needs further clarification or inputs you may mail sumanapala@gmail.com) </SPAN>\n" );
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