document.write( "Question 1141127: If a, b, c, and d are in G. P., Then show that (a+b)², (b+c)² and (c+d)² are also in G. P \n" ); document.write( "

Algebra.Com's Answer #761663 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Since a, b, c, and d are in geometric progression, call them a, ar, ar^2, and ar^3. Then you need to show that (a+ar)^2, (ar+ar^2)^2, and (ar^2+ar^3)^2 are in geometric progression. That is almost obvious.

\n" ); document.write( " $\"%28ar%2Bar%5E2%29%5E2+=+%28r%28a%2Bar%29%29%5E2+=+r%5E2%28a%2Bar%29%5E2\"$ --> The second term is r^2 times the first.

\n" ); document.write( " $\"%28ar%5E2%2Bar%5E3%29%5E2+=+%28r%5E2%28a%2Bar%29%29%5E2+=+r%5E4%28a%2Bar%29%5E2\"$ --> The third term is r^4 = (r^2)^2 times the first.

\n" ); document.write( "The common ratio between the terms of the new sequence is r^2. \n" ); document.write( "

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