Solving Sequences and Series Homework

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SUMMARY

The discussion revolves around solving a homework problem involving sequences and series, specifically filling in blanks to create an arithmetic sequence, a geometric sequence, and a non-arithmetic/non-geometric sequence. The participants initially attempted a Fibonacci-type sequence but found it ineffective. Ultimately, they concluded that a quadratic relationship could be a viable solution for the non-standard sequence. The problem emphasizes understanding different types of sequences and their properties.

PREREQUISITES
  • Understanding of arithmetic sequences
  • Knowledge of geometric sequences
  • Familiarity with quadratic relationships
  • Basic concepts of sequences and series
NEXT STEPS
  • Research methods for constructing arithmetic sequences
  • Learn about geometric sequence properties and formulas
  • Explore quadratic sequences and their general term formulation
  • Study non-standard sequences and their characteristics
USEFUL FOR

Students studying mathematics, educators teaching sequences and series, and anyone looking to enhance their problem-solving skills in algebra.

Char. Limit
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Homework Statement


So I was helping my roommate with his homework, and it has the following problem:

Fill in the blanks so that

___, 8, ___, ___, 27, ___, ...

is

a. an arithmetic sequence.
b. a geometric sequence.
c. a sequence that is neither arithmetic nor geometric, for which you are able to write a general term.


Homework Equations





The Attempt at a Solution



We tried a Fibonnaci-type sequence, but that really didn't work. And we don't know any other types of sequences. Should I try some sort of quadratic relationship?
 
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Never mind, solved.
 

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