document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187314>Question 1187314</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first term of an arithmetic progression is 12 and the sum of the first 16 terms is 282.<BR>\n" );
document.write( "a) Find the common difference of this progression.<BR>\n" );
document.write( "The first, fifth and nth term of this arithmetic progression are the first, second and third<BR>\n" );
document.write( "term respectively of a geometric progression.<BR>\n" );
document.write( "b) Find the common ratio of the geometric progression and the value of n. </SPAN>\n" );
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document.write( "The first 16 terms are<br><BR>\n" );
document.write( "a, a+d, a+2d, ..., a+14d, a+14d<br><BR>\n" );
document.write( "Combining like terms, the sum of the first 16 terms is<br><BR>\n" );
document.write( "16a + (1+2+3+...+14+15)d = 16a+120d<br><BR>\n" );
document.write( "The first term is 12; the sum of the first 16 terms is 282:<BR>\n" );
document.write( "16(12)+120d = 282<BR>\n" );
document.write( "192+120d = 282<BR>\n" );
document.write( "120d = 90<BR>\n" );
document.write( "d = 3/4<br><BR>\n" );
document.write( "ANSWER a): the common difference is 3/4<br><BR>\n" );
document.write( "1st term: 12<BR>\n" );
document.write( "5th term: 12+4(3/4) = 12+3 = 15<br><BR>\n" );
document.write( "The 1st and 5th terms of the arithmetic progression are the 1st and second terms of a geometric progression.<br><BR>\n" );
document.write( "common ratio: 15/12 = 5/4<br><BR>\n" );
document.write( "3rd term in the geometric progression: 15(5/4) = 75/4 = 12+27/4 = 12+9d, which is the 10th term of the arithmetic progression.<br><BR>\n" );
document.write( "The 3rd term of the geometric progression is the 10th term of the arithmetic progression.<br><BR>\n" );
document.write( "ANSWER b): common ratio 3/4; n=10<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );