document.write( "Question 1170329: The 6th term of Ap is 35 and the 13th term is 77. find the 20th term \n" ); document.write( "

Algebra.Com's Answer #795197 by ikleyn(52776) $\"\"$ $\"About$

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document.write( "There are 13 - 6 = 7  intervals (gaps)  between the 6th and 13th terms of the AP.\r\n" );
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document.write( "Therefore, the width of each gap is   =  = 6.\r\n" );
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document.write( "It means that the common difference of the arithmetic progression is 6.\r\n" );
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document.write( "Next, there are  20-13 = 7 intervals (gaps) between the 13th and 20th terms;\r\n" );
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document.write( "therefore, the 20th term is   + 7*6 = 77 + 42 = 119.\r\n" );
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document.write( "ANSWER.  The 20th term is 119.\r\n" );
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document.write( "Another possible solution is to notice that the 13th term of an AP is exactly half of the way between the 6th and 20th terms\r\n" );
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document.write( "It means that the distance from the 13th term to the 20th term is exactly the same as between the 6th term and 13th term\r\n" );
document.write( "which is 77-35 = 42.\r\n" );
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document.write( "Therefore, we add 42 to 77 and obtain the 20th term as  77+42 = 119,  getting the same answer.\r\n" );
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