SOLUTION: First question: A geometric sequence consisting of four terms in which ratio is positive, the sum of the first two terms is 8 and the sum of the last two terms is 72. Find the seq

Question 1037774: First question:
A geometric sequence consisting of four terms in which ratio is positive, the sum of the first two terms is 8 and the sum of the last two terms is 72. Find the sequence
Second question:
Find three numbers in a geometric sequence whose sum is 42 and whose product is 512
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
For the first question:
and ==> , and .
Dividing the second equation by the first equation, we get , which means r = 3. (r = -3 is not acceptable, as the ratio should be positive.)
The sequence is thus 2, 6, 18, 54.

For the second question:
and
The second equation gives , which implies that , after taking cube roots of both sides.
The first equation is equivalent to
. Dividing this equation with , we get

==> <==> <==> r = 1/4 or 4.
If r = 1/4, the sequence is 32, 8, 2.
If r = 4, the sequence is 2, 8, 32.
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