document.write( "Question 41934: Find four geometric means between 4096 and 972.\r
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Algebra.Com's Answer #27086 by AnlytcPhil(1806)\"\" \"About 
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Find four geometric means between 4096 and 972.\r\n" );
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document.write( "This means to make a geometric sequence with 6 terms with\r\n" );
document.write( "the 1st term being 4096, and the 5th term 972, and four\r\n" );
document.write( "terms (geometric means) between them. In other words,\r\n" );
document.write( "you are to find the missing four numbers in\r\n" );
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document.write( "4096, ____, ____, ____, ____, 972\r\n" );
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document.write( "so that the six terms will be a geometric sequence.\r\n" );
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document.write( "We use the formula\r\n" );
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document.write( "an = a1rn-1\r\n" );
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document.write( "with n=6\r\n" );
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document.write( "a6 = a1r6-1\r\n" );
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document.write( "a6 = a1r5\r\n" );
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document.write( "Now we substitute a6 = 972, and a1 = 4096\r\n" );
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document.write( "972 = 4096r5\r\n" );
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document.write( "972/4096 = r5\r\n" );
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document.write( "243/1024 = r5\r\n" );
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document.write( "35/45 = r5\r\n" );
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document.write( "(3/4)5 = r5\r\n" );
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document.write( "Take fifth roots of both sides\r\n" );
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document.write( "3/4 = r\r\n" );
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document.write( "So we multiply the 1st term, a1, which is 4096,\r\n" );
document.write( "by r, which is 3/4,  and get\r\n" );
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document.write( "a2 = 4096(3/4) = 3072\r\n" );
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document.write( "Then we multiply the 2nd term, a2, which is 3072,\r\n" );
document.write( "by r, which is 3/4,  and get\r\n" );
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document.write( "a3 = 3072(3/4) = 2304\r\n" );
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document.write( "Then we multiply the 3rd term, a3, which is 2304,\r\n" );
document.write( "by r, which is 3/4,  and get\r\n" );
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document.write( "a4 = 2304(3/4) = 1728\r\n" );
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document.write( "Then we multiply the 4th term, a4, which is 1728,\r\n" );
document.write( "by r, which is 3/4,  and get\r\n" );
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document.write( "a5 = 1728(3/4) = 1296\r\n" );
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document.write( "Then finally, as a check, we multiply the 5th term, a5,\r\n" );
document.write( "which is 1296, to see if we get the 6th term, which is\r\n" );
document.write( "given as 972, by r, which is 3/4,  and see if we get\r\n" );
document.write( "972.\r\n" );
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document.write( "a6 = 1296(3/4) = 972\r\n" );
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document.write( "Yes we do, so the geometric sequence is\r\n" );
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document.write( "4096, 3072, 2304, 1728, 1296, 972\r\n" );
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document.write( "and the four geometric means between the 1st and 6th terms are\r\n" );
document.write( "the four terms between them:\r\n" );
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document.write( "3072, 2304, 1728, and 1296 \r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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