What is the value of m in the given geometric sequence?

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The discussion centers on finding the value of m in a geometric sequence formed by three terms from an arithmetic sequence defined by the sum formula sn=4n²-2n. To find the terms, the nth term can be calculated using un = sn - sn-1. Specifically, u2 and u32 are derived from the sum formula by calculating s2, s1, s32, and s31, then subtracting accordingly. The relationship between the terms in the geometric sequence is established through the equation u_m/u2 = u32/u_m. The conversation emphasizes the need to apply properties of geometric sequences to solve for m.
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the sum of the first n terms of an arithmetic sequence {un} is given by the
formula sn=4n2-2n. three terms of this secuence, u2 um and u32 are conscutive terms en a geomtric sequence. find m.

Yea, I am really confused... please help :-)
 
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you can find tn by

u_{n} = s_{n} - s_{n-1}

Then find u_{m} by applying properties of geometric sequence. work back and find m
 
In particular, u_2= s_2- s_1. Find s_2 and s_1 from the formula you are given and subtract. u_{32}= s_{32}- s_{31}. Again find those and subtract. Now you know two terms of a geometric sequence you can find the term between them. \frac{u_m}{u_2}= \frac{u_{32}}{u_m}.
 
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