SOLUTION: 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

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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
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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.

%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.

%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.

The common ratio between the terms of the new sequence is r^2.