Homework Help: math!

Posted by Anonymous on Wednesday, October 18, 2006 at 2:16pm.

determine two geometreic sequences whose first terms are 18x-9, 2x+8 and x-1

how would I go about and do this question?
I have no idea! so a little help would be really helpful! thanks!

A geometric sequence looks like
a, ar, ar², ar³, ..., arⁿ, ...
where a is usually called the base and r is the common ratio.

If the first three terms are 18x-9, 2x+8 and x-1 then
(2x+8)/(18x-9) = (x-1)/(2x+8)
i.e., the ratio of t_n/t_n-1 is the common ratio.
So solve
(2x+8)*(2x+8)=(18x-9)*(x-1) for x.
Then substitute the values of x into the first 3 terms to determine what they are, then follow the above to determine the common ratio, the base, then the general or n^th term.

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