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

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Homework Help Overview

The problem involves finding the value of m in a geometric sequence formed by three consecutive terms of an arithmetic sequence, where the sum of the first n terms of the arithmetic sequence is defined by a specific formula.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss deriving individual terms of the arithmetic sequence from the given sum formula and relate them to the properties of a geometric sequence. There are attempts to express terms in terms of n and explore relationships between the terms.

Discussion Status

Some participants have offered methods to find individual terms of the arithmetic sequence and suggested how to relate them to the geometric sequence. There is a sense of confusion expressed by the original poster, indicating that the discussion is ongoing without a clear resolution yet.

Contextual Notes

There is mention of a specific formula for the sum of the arithmetic sequence, and participants are working with the constraints of that formula to derive necessary terms. The original poster expresses difficulty in navigating the problem setup.

hostergaard
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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

[tex]u_{n} = s_{n} - s_{n-1}[/tex]

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

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