document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203626>Question 1203626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the problem.\r<BR>\n" );
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document.write( "underbrace(5 + 8 + 11 + 14 + . . . + 299 + 302) = <BR>\n" );
document.write( "100 terms </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839329 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (5 + 8 + 11 + 14 + . . . + 299 + 302) = \r<BR>\n" );
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document.write( "This is an arithmetic sequence because the common difference between each consecutive term is constant  The sum of an arithmetic sequence  is given by the formula:\r<BR>\n" );
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document.write( "Sn= (n/2) * [2a + (n-1)d]\r<BR>\n" );
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document.write( "n is the number of terms.<BR>\n" );
document.write( "a is the first term.  -------------a= 5<BR>\n" );
document.write( "d is the common difference ------- d=3<BR>\n" );
document.write( "First we have  to find the number of terms in the sequence ,n\r<BR>\n" );
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document.write( "To find n, we use the formula for the nth term of an arithmetic sequence:<BR>\n" );
document.write( "nth term = a + (n-1)d\r<BR>\n" );
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document.write( "Plug values\r<BR>\n" );
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document.write( "302 = 5 + (n-1) * 3\r<BR>\n" );
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document.write( "302 - 5 = (n-1) * 3<BR>\n" );
document.write( "297 = (n-1) * 3\r<BR>\n" );
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document.write( "Divide  by 3\r<BR>\n" );
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document.write( "99 = n - 1\r<BR>\n" );
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document.write( "So n = 100\r<BR>\n" );
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document.write( "There are 100 terms in this serquence. n=100\r<BR>\n" );
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document.write( "Now, put these values into the sum formula:\r<BR>\n" );
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document.write( "Sn = (100/2) * [2 * 5 + (100-1) * 3]<BR>\n" );
document.write( "Sn = (50) * [10 + 99 * 3]<BR>\n" );
document.write( "Sn = 50 * (10 + 297)<BR>\n" );
document.write( "Sn = 50 * 307<BR>\n" );
document.write( "Sum = 15,350\r<BR>\n" );
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document.write( "Therefore, the sum of the given terms  is 15,350.\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );