Geometric Progression w/ 2m – 8, 2m + 4, 5m – 2 being conseq. terms

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Alfonsobonso

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Geometric Progression w/ 2m – 8, 2m + 4, 5m – 2 being conseq. terms

Given that 2m – 8, 2m + 4 and 5m – 2 are successive terms of a geometric sequence. Find the value of m and thus the summation of the first 10 elements.






I don't want the answer to this question, rather just whether it is actually possible. So far I have found m = 10 and r = 2 (or alternatively m = 0 and r = -1/2) which gives the consecutive terms listed in the question values of 12, 24 and 48 (or -8, 4 and -2).


But to work out the summation of the first 10 elements (using the formula (a(r^10-1))/(r-1) ) then surely I need to know a. As the question states that the terms are consecutive but doesn't give information about where in the sequence they appear, is it even possible to work out a and hence the summation? If I understand this correctly then a could be 12, but it could as easily be 6 or 3 or . . . . .


NB I shouldn't assume anything - so I can't assume that 2m-8 is the first term.


Thanks.
 
Alfonsobonso said:
Given that 2m – 8, 2m + 4 and 5m – 2 are successive terms of a geometric sequence. Find the value of m and thus the summation of the first 10 elements.






I don't want the answer to this question, rather just whether it is actually possible. So far I have found m = 10 and r = 2 (or alternatively m = 0 and r = -1/2) which gives the consecutive terms listed in the question values of 12, 24 and 48 (or -8, 4 and -2).


But to work out the summation of the first 10 elements (using the formula (a(r^10-1))/(r-1) ) then surely I need to know a. As the question states that the terms are consecutive but doesn't give information about where in the sequence they appear, is it even possible to work out a and hence the summation? If I understand this correctly then a could be 12, but it could as easily be 6 or 3 or . . . . .


NB I shouldn't assume anything - so I can't assume that 2m-8 is the first term.


Thanks.
Click to expand...
In my Opinion, you are ABSOLUTELY correct.

The question regarding the summation is incomplete.

Please contact the instructor for further explanation.
 
Subhotosh Khan said:
In my Opinion, you are ABSOLUTELY correct.

The question regarding the summation is incomplete.

Please contact the instructor for further explanation.
Click to expand...


Believe me, I have! So many times now, my head is spinning! I asked whether the question should mention that the terms given are the first three successive terms but was told "No, if this information was needed, it would be stated clearly in the question."

I think he's wrong but i wanted to get advice from elsewhere before I approach him about it again!
 
Alfonsobonso said:
… 2m – 8, 2m + 4 and 5m – 2 are successive terms of a geometric sequence …
Click to expand...
I agree with Subhotosh; there's not enough information given, to sum the first ten terms.

Additionally, as you've discovered, there are two different geometric sequences containing the three given terms. They haven't even told us which one they're talking about! :roll:
 
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