document.write( "Question 1043415: Find a number x which, when added to each of the numbers 21, 27, and 29 in this order, produces three numbers which are in a geometric progression. \n" ); document.write( "
Algebra.Com's Answer #658555 by rothauserc(4718)\"\" \"About 
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21, 27, 29
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\n" ); document.write( "use the definition for any term in a geometric progression
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\n" ); document.write( "an = a0 * r^(n-1)
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\n" ); document.write( "a0 = 21+x
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\n" ); document.write( "1) a1 = 27+x = (21+x) * r
\n" ); document.write( "2) a2 = 29+x = (21+x) * r^2
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\n" ); document.write( "solve equation 1 for r
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\n" ); document.write( "r = (27+x) / (21+x)
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\n" ); document.write( "substitute for r in equation 2
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\n" ); document.write( "29+x = (21+x) * (27+x)^2 / (21+x)^2
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\n" ); document.write( "29+x = (27+x)^2 / (21+x)
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\n" ); document.write( "(29+x)*(21+x) = (27+x)^2
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\n" ); document.write( "x^2 +50x +609 = x^2 +54x +729
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\n" ); document.write( "4x = -120
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\n" ); document.write( "x = -30
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\n" ); document.write( "we add -30 to each number
\n" ); document.write( "-9, -3, -1
\n" ); document.write( "the common ratio is 1/3
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