SOLUTION: Find all geometric sequences in which t3 + t4 = 36 and t5 + t6 = 144 I know one could be t1=3 t2=6 t3=12 t4=24 t5=48 t6=96 That would fit the question, but i'm assuming the

Question 762771: Find all geometric sequences in which t3 + t4 = 36 and t5 + t6 = 144

I know one could be t1=3 t2=6 t3=12 t4=24 t5=48 t6=96
That would fit the question, but i'm assuming there's more than one geometric sequence that fits? There is two questions like this on my assignment. Don't know how to go about finding multiple sequences
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
The way to solved it could be this one:

and

These can be factored to
and

Therefore,
and

Setting these equal to each other and cross multiplying gives
, or

One solution is for to be , but that obviously won't work.

So, dividing through by gives , so can be either or .

Using these with the previous equations gives the value of ,
and therefore the sequence.
..=>..=>..=>..=>
same here
..=>..=>..=>..=>
geometric sequences is

...and so on
check if and

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