document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=675848>Question 675848</A>: <I><SPAN STYLE=\"word-break: break-all;\"> is the sequence 1,1,1,1,1,1,1 a arithmetic sequence </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420099 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=420099\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Definition of Arithmetic Sequence\r<BR>\n" );
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document.write( "    Arithmetic sequence is a sequence of numbers that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=has ALIGN=MIDDLE  ALT=\"has\"   DISABLED_style= \"max-width:90%; height:auto;\" > a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=constant ALIGN=MIDDLE  ALT=\"constant\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=difference ALIGN=MIDDLE  ALT=\"difference\"   DISABLED_style= \"max-width:90%; height:auto;\" > between every two consecutive terms.<BR>\n" );
document.write( "    In other words, arithmetic sequence is a sequence of numbers in which <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=each ALIGN=MIDDLE  ALT=\"each\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+term ALIGN=MIDDLE  ALT=\"+term\"   DISABLED_style= \"max-width:90%; height:auto;\" > except the first term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" > the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=result ALIGN=MIDDLE  ALT=\"result\"   DISABLED_style= \"max-width:90%; height:auto;\" > of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=adding ALIGN=MIDDLE  ALT=\"adding\"   DISABLED_style= \"max-width:90%; height:auto;\" > the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" > number, called the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=common ALIGN=MIDDLE  ALT=\"common\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+difference ALIGN=MIDDLE  ALT=\"+difference\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to the preceding term.\r<BR>\n" );
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document.write( "in your case, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=common ALIGN=MIDDLE  ALT=\"common\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+difference ALIGN=MIDDLE  ALT=\"+difference\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=0 ALIGN=MIDDLE  ALT=\"d=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the rule for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n-th ALIGN=MIDDLE  ALT=\"n-th\"   DISABLED_style= \"max-width:90%; height:auto;\" > term of a pattern is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E0+%2B+0 ALIGN=MIDDLE  ALT=\"n%5E0+%2B+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the sum of which is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%28n%29+=+%28n%2F2%29+%282a%5B0%5D+%2B+%28n-1%29d%29+=%28n%2F2%29+%28a%5B0%5D+%2B+a%5Bn%5D%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "let's check the sum of all terms given in your sequence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%287%29+=+%287%2F2%29+%281+%2B+1%29+ ALIGN=MIDDLE  ALT=\"S%287%29+=+%287%2F2%29+%281+%2B+1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%287%29+=+%287%2F2%29+%282%29+ ALIGN=MIDDLE  ALT=\"S%287%29+=+%287%2F2%29+%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%287%29+=+7+ ALIGN=MIDDLE  ALT=\"S%287%29+=+7+\"   DISABLED_style= \"max-width:90%; height:auto;\" >..which is true\r<BR>\n" );
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document.write( "so, the answer is yes, the sequence 1,1,1,1,1,1,1 is a arithmetic sequence\r<BR>\n" );
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