document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195430>Question 1195430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first term of an AP is 3. Given that the sum of the first 6 terms is 48 and that the sum of all the terms is 168 .calculate the common difference,the number of terms in the AP and the last term  </SPAN>\n" );
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document.write( "The sum of an AP is the number of terms, multiplied by the average of the first and last terms.  Given first term 3 and sum the first six terms 48, the average is 48/6 = 8.  If the 6th term is x, then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2Bx%29%2F2=8 ALIGN=MIDDLE  ALT=\"%283%2Bx%29%2F2=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Bx=16 ALIGN=MIDDLE  ALT=\"3%2Bx=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=13 ALIGN=MIDDLE  ALT=\"x=13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the 6th term is 13.<br><BR>\n" );
document.write( "That 6th term, 13, is the first term, 3, plus the common difference, d, 5 times:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13=3%2B5d ALIGN=MIDDLE  ALT=\"13=3%2B5d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10=5d ALIGN=MIDDLE  ALT=\"10=5d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2 ALIGN=MIDDLE  ALT=\"d=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the AP has first term 3 and common difference 2.<br><BR>\n" );
document.write( "Now let n be the number of terms in the whole sequence.  The last term is the first term, 3, plus the common difference, d, (n-1) times:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B%28n-1%292=3%2B2n-2=2n%2B1 ALIGN=MIDDLE  ALT=\"3%2B%28n-1%292=3%2B2n-2=2n%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The sum of all the terms, 168, is the number of terms, n, times the average of the first and last terms:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=n%283%2B%282n%2B1%29%29%2F2=n%28n%2B2%29=168 ALIGN=MIDDLE  ALT=\"S=n%283%2B%282n%2B1%29%29%2F2=n%28n%2B2%29=168\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n=168 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n=168\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E2%2B2n-168=0 ALIGN=MIDDLE  ALT=\"n%5E2%2B2n-168=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B14%29%28n-12%29=0 ALIGN=MIDDLE  ALT=\"%28n%2B14%29%28n-12%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=12 ALIGN=MIDDLE  ALT=\"n=12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The number of terms in the whole sequence is 12.<br><BR>\n" );
document.write( "The last (12th) term is 3+11(2)=25.<br><BR>\n" );
document.write( "ANSWERS:<BR>\n" );
document.write( "common difference: 2<BR>\n" );
document.write( "number of terms: 12<BR>\n" );
document.write( "last term: 25<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "(Sum = number of terms times average of first and last)<BR>\n" );
document.write( "12((3+25)/2)=12(28/2)=12*14=168<br><BR>\n" );
document.write( " </SPAN>\n" );
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