document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210336>Question 1210336</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) The eighth term of an Arithmetic Progression (A.P) is 46 and the sum of the first eight terms is 200. Find the:<BR>\n" );
document.write( "(i) first term; <BR>\n" );
document.write( "(ii) sum of the first 12 terms. \r<BR>\n" );
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document.write( "(b) The points X(70°S, 60°E) and Y(7°S, 60°E) lies on the surface of the earth. <BR>\n" );
document.write( "(i) Illustrate the information in a diagram. <BR>\n" );
document.write( "(ii) Find the distance between X and Y along the meridian. <BR>\n" );
document.write( "[Take л = 22/7 and R = 6,400 km] </SPAN>\n" );
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document.write( "(a)<br><BR>\n" );
document.write( "The 8th term is 46; the sum of the first 8 terms is 200.<br><BR>\n" );
document.write( "The sum of the first 8 terms is the number of terms (8) times the average of all the terms; the average of all the terms is the average of the first and last.  So to find the first term a:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2B46%29%2F2=200%2F8=25 ALIGN=MIDDLE  ALT=\"%28a%2B46%29%2F2=200%2F8=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B46=50 ALIGN=MIDDLE  ALT=\"a%2B46=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The 1st term is 4; the 8th term, 46, is the first term plus the common difference d 8-1 = 7 times.  The common difference d is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%2846-4%29%2F%288-1%29=42%2F7=6 ALIGN=MIDDLE  ALT=\"d=%2846-4%29%2F%288-1%29=42%2F7=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The 12th term is the 8th term, 46, plus the common difference 12-8 = 4 times:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=46%2B4%286%29=46%2B24=70 ALIGN=MIDDLE  ALT=\"46%2B4%286%29=46%2B24=70\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The sum of the first 12 terms is the number of terms, 12, times the average of the first and 12th terms:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%28%284%2B70%29%2F2%29=12%2837%29=444 ALIGN=MIDDLE  ALT=\"12%28%284%2B70%29%2F2%29=12%2837%29=444\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWERS: first term 4; sum of first 12 terms 444<br><BR>\n" );
document.write( "(b)<br><BR>\n" );
document.write( "The difference between the two points is 70-7 = 63 degrees in latitude.<br><BR>\n" );
document.write( "Latitudes range from -90 degrees (South Pole) to +90 degrees (North Pole), a range of 180 degrees.<br><BR>\n" );
document.write( "The distance between the two points is (63/180)=(7/20) of the distance from the South to North Poles, which is (7/20) of the length of a semicircular arc with radius 6400 km.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%287%2F20%29%2822%2F7%29%286400%29=%281%2F2%29%2811%2F10%29%286400%29=%2811%2F20%29%286400%29=11%28320%29=3520 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 3520 km<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );