document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204428>Question 1204428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man borrows 2,00 and agrees to repay with a total interest of 340 in 12 monthly instalment, each instalment being less than the preceding instalment by 10, What should be his first instalment? </SPAN>\n" );
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document.write( "I assume you meant to write 2,000 instead of 2,00\r<BR>\n" );
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document.write( "a = first installment = first term of arithmetic sequence\r<BR>\n" );
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document.write( "n = 12 = number of payments<BR>\n" );
document.write( "d = -10 = common difference, since the payment amounts drop by 10 each time.\r<BR>\n" );
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document.write( "Sn = sum of first n terms of arithmetic sequence, aka arithmetic progression (AP)<BR>\n" );
document.write( "Sn = 2000+340 = 2340 total needs to be paid back\r<BR>\n" );
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document.write( "Sn = (n/2)*(2*a + d(n-1))<BR>\n" );
document.write( "2340 = (12/2)*(2*a - 10(12-1))<BR>\n" );
document.write( "2340 = 6*(2a-110)<BR>\n" );
document.write( "2340 = 12a-660<BR>\n" );
document.write( "12a-660 = 2340<BR>\n" );
document.write( "12a = 2340+660<BR>\n" );
document.write( "12a = 3000<BR>\n" );
document.write( "a = 3000/12<BR>\n" );
document.write( "a = <font color=red>250</font>\r<BR>\n" );
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document.write( "We can use the \"sequence\" command in GeoGebra to generate this arithmetic progression<BR>\n" );
document.write( "250, 240, 230, 220, 210, 200, 190, 180, 170, 160, 150, 140<BR>\n" );
document.write( "A spreadsheet is another option.\r<BR>\n" );
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document.write( "Then add up the values and we should get to 2340<BR>\n" );
document.write( "250+240+230+220+210+200+190+180+170+160+150+140 = 2340<BR>\n" );
document.write( "We have confirmed the answer.<BR>\n" );
document.write( "Or a shortcut<BR>\n" );
document.write( "(n/2)*(1st term + 12th term) = (12/2)*(250 + 140) = 2340\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>250</font><BR>\n" );
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