Finding the general expression of the nth term

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Homework Help Overview

The problem involves finding the general expression for the nth term of a sequence defined by the terms 11, 21, 35, 53, 75, 101, where n is a positive integer. The context is related to sequences and series in mathematics.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Some participants question whether the sequence could be arithmetic or geometric. Others suggest forming a new sequence from the differences between successive terms to analyze the pattern.

Discussion Status

The discussion includes various attempts to identify the nature of the sequence and explore the differences between terms. Some participants have proposed generating expressions based on the differences, while others express uncertainty about how to derive a general expression without trial and error.

Contextual Notes

There is a mention of the challenge in determining a general expression and the potential need for trial and error, indicating a lack of clear direction in the problem-solving process.

superconduct
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Homework Statement


Given successive terms of numbers starting from the 1st term:
11, 21, 35, 53, 75, 101,...
What is the general expression of the nth term? where n is positive integer

Homework Equations


/

The Attempt at a Solution


Can't find a good attempt.
 
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Could this be an arithmetic or geometric sequence??
 
superconduct said:

Homework Statement


Given successive terms of numbers starting from the 1st term:
11, 21, 35, 53, 75, 101,...
What is the general expression of the nth term? where n is positive integer

Homework Equations


/

The Attempt at a Solution


Can't find a good attempt.

Form a new sequence from the differences between successive terms.
 
sorry I don't know...

how will you determine a general expression for it in this problem without trial and error?

is it like finding a needle in the ocean?
 
look at the terms, then form a sequences of differences and what do you get?

10 , 14, 18, 22, 26 ...

look at the differences as a sequence and what do you see?

write an expression to generate the differences sequence

term(n)= term(0) + 4*(n-1) where n=1, 2, 3, 4...

then write an expression to generate your sequence using the differences expression

TERM(n) = TERM(0) + ...
 
Ouw... I think you can use the Sn to calculate the Un...
 

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