document.write( "Question 1185943: 1.the geometric mean between the first two terms is 32.if the third term is 4.find the first term \n" ); document.write( "

Algebra.Com's Answer #816865 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The geometric mean between the first TWO terms is 32, and the third term is 4; from that we can conclude that the common ratio is less than 1.

\n" ); document.write( "Then, given that the geometric mean between the first two terms is 32, along with the fact that the common ratio is less than 1, we can do this:

\n" ); document.write( "Let the first term be 32/x
\n" ); document.write( "Let the second term be 32x

\n" ); document.write( "Then the first three terms of the geometric sequence are

\n" ); document.write( "32/x, 32x, 4

\n" ); document.write( "Now use the fact that the second term is the geometric mean between the first and third:

\n" ); document.write( " $\"%2832x%29%5E2=%2832%2Fx%29%284%29\"$
\n" ); document.write( " $\"1024x%5E2=128%2Fx\"$
\n" ); document.write( " $\"x%5E3=128%2F1024=1%2F8\"$
\n" ); document.write( " $\"x=1%2F2\"$

\n" ); document.write( "The common ratio is 1/2; the terms are
\n" ); document.write( "32/x = 32/(1/2) = 64
\n" ); document.write( "32x = 32(1/2) = 16
\n" ); document.write( "4

\n" ); document.write( "ANSWER: The first term is 64

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