SOLUTION: the three consecutive terms in a the G.P are the second third of and sixth term of an A.P find the common ratio?

Question 1083648: the three consecutive terms in a the G.P are the second third of and sixth term of an A.P find the common ratio?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Let's define a couple of variables:
= the first of the three consecutive terms in the G.P.
= the common ratio of the G.P.
Then, the next two (consecutive) terms in the G.P are
= the second of the three consecutive terms in the G.P. ,
and = the third of the three consecutive terms in the G.P.
The problem probably meant to tell us that
= the second term of the A.P.
= the third term of the A.P.
That makes the common difference of the A.P.
The problem probably meant to tell us that
= the sixth term of the A.P.
That would make it common differences more than the second term of the A.P.:

We can simplify and solve for the equation above

We have 3 possible options:
1) and is undefined,
probably not the answer expected.
All the terms of the A.P. and the G.P. would be zero.
2) , also probably not the answer expected.
All the terms of the A.P. and the G.P. would be , whatever that value is.
3) is probably the expected answer.
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