document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=755524>Question 755524</A>: <I><SPAN STYLE=\"word-break: break-all;\"> sum of first 20 terms of an arithmetic sequence is 900. sixth term is 27. what is<BR>\n" );
document.write( " its fifteenth term and common difference.<BR>\n" );
document.write( " </SPAN>\n" );
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document.write( "sum of first 20 terms of an arithmetic sequence is 900. sixth term is 27. what is<BR>\n" );
document.write( "its fifteenth term and common difference.<BR>\n" );
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document.write( "A:<BR>\n" );
document.write( "In arithmetic sequence, the sum of the first n terms is equal to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D ALIGN=MIDDLE  ALT=\"S%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2F2%29%28a%5B1%5D+%2B+a%5Bn%5D%29 ALIGN=MIDDLE  ALT=\"%28n%2F2%29%28a%5B1%5D+%2B+a%5Bn%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The sixth term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B6%5D ALIGN=MIDDLE  ALT=\"a%5B6%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 27, if the common difference is d then the first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 27 - 5d and the 20th term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B20%5D ALIGN=MIDDLE  ALT=\"a%5B20%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 27 + 14d.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5B20%5D ALIGN=MIDDLE  ALT=\"S%5B20%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2F2%29%28a%5B1%5D+%2B+a%5B20%5D%29 ALIGN=MIDDLE  ALT=\"%2820%2F2%29%28a%5B1%5D+%2B+a%5B20%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "900 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2F2%29%28%2827+-+5d%29+%2B+%2827+%2B+14d%29%29 ALIGN=MIDDLE  ALT=\"%2820%2F2%29%28%2827+-+5d%29+%2B+%2827+%2B+14d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "900 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%289d+%2B+54%29 ALIGN=MIDDLE  ALT=\"10%289d+%2B+54%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "9d + 54 = 90<BR>\n" );
document.write( "d = 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B1%5D ALIGN=MIDDLE  ALT=\"a%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 27 - 5(4) = 7<BR>\n" );
document.write( "The nth term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5Bn%5D ALIGN=MIDDLE  ALT=\"a%5Bn%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7 + 4(n - 1) = 4n + 3<BR>\n" );
document.write( "The 15th term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B15%5D ALIGN=MIDDLE  ALT=\"a%5B15%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4(15) + 3 = 63<BR>\n" );
document.write( "Here are the answers: <BR>\n" );
document.write( "15th term: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2863%29 ALIGN=MIDDLE  ALT=\"highlight%2863%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and common difference, d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284%29 ALIGN=MIDDLE  ALT=\"highlight%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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