document.write( "Question 1086119: The arithmetic means between the 6th and 9th term of an arithmetic sequence are 13.5 and 15 (in what order) what are the first and 20th terms of the sequence? \n" ); document.write( "
Algebra.Com's Answer #700296 by Edwin McCravy(20055)\"\" \"About 
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document.write( "The arithmetic means between the 6th and 9th terms are the \r\n" );
document.write( "7th and 8th terms of the arithmetic sequence.  So we are \r\n" );
document.write( "asked to put the numbers in the two blanks below with \r\n" );
document.write( "question marks:\r\n" );
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document.write( " ? ,___,___,___,___,___,13.5, 15,___,___,___,___,___,___,___,___,___,___,___, ? \r\n" );
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document.write( "We know that the common difference d, is the difference between\r\n" );
document.write( "any two consecutive terms.  We have the 7th and 8th terms, which\r\n" );
document.write( "are consecutive, so the common difference = d = 15-13.5 = 1.5.\r\n" );
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document.write( "The formula for the nth term of an arithmetic sequence is:\r\n" );
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document.write( "an = a1 + (n - 1)d\r\n" );
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document.write( "Substitute n = 7 and d = 1.5\r\n" );
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document.write( "a7 = a1 + (7 - 1)(1.5)\r\n" );
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document.write( "Substitute a7 = 13.5 and simplify\r\n" );
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document.write( "13.5 = a1 + (6)(1.5)\r\n" );
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document.write( "13.5 = a1 + 9\r\n" );
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document.write( " 4.5 = a1    <-- the first term\r\n" );
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document.write( "Now we want to find the 20th term, so we use the formula\r\n" );
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document.write( "an = a1 + (n - 1)d\r\n" );
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document.write( "and substitute n = 20, d = 1.5 and  a1 = 4.5\r\n" );
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document.write( "a20 = 4.5 + (20 - 1)(1.5)\r\n" );
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document.write( "a20 = 4.5 + (19)(1.5)\r\n" );
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document.write( "a20 = 4.5 + 28.5\r\n" );
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document.write( "a20 = 33   <-- 20th term\r\n" );
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document.write( "Checking, here's the whole sequence through the 20th term:\r\n" );
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document.write( "4.5, 6,7.5, 9,10.5,12,13.5,15,16.5,18,19.5,21,22.5,24,25.5,27,28.5,30,31.5,33\r\n" );
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document.write( "Edwin
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