document.write( "Question 898312: Find all the possible values of x such that this sequence is geometric: x,12,9x \n" ); document.write( "
Algebra.Com's Answer #544736 by DrBeeee(684)\"\" \"About 
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In a geometric sequence each term is a constant, say c, times the previous term.
\n" ); document.write( "For the given sequence
\n" ); document.write( "(1) x, 12 , 9x we get
\n" ); document.write( "(2) 12 = cx or
\n" ); document.write( "(3) c = 12/x
\n" ); document.write( "Then we have for the third term
\n" ); document.write( "(4) 9x = (12/x)*12 or
\n" ); document.write( "(5) 9x^2 = 12^2 or
\n" ); document.write( "(6) x^2 = (12^2)/(3^2) or
\n" ); document.write( "(7) x = 12/3 or
\n" ); document.write( "(8) x = 4
\n" ); document.write( "Let's check this. Using (3) we get
\n" ); document.write( "(9) c = 12/4 or
\n" ); document.write( "(10) c = 3
\n" ); document.write( "The sequnce should be
\n" ); document.write( "(11) 4, 3*4, 3*3*4 or
\n" ); document.write( "(12) 4, 12, 36 or
\n" ); document.write( "(13) 4, 12, 9*4
\n" ); document.write( "I believe that x = 4 is the only possible solution. \n" ); document.write( "
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