Finding the general expression of the nth term

AI Thread Summary
The discussion focuses on finding the general expression for the nth term of the sequence 11, 21, 35, 53, 75, 101. Participants suggest analyzing the differences between successive terms, which yield a new sequence of 10, 14, 18, 22, and 26. This difference sequence indicates a quadratic relationship, prompting the formulation of an expression for the differences. A proposed expression for the nth term is derived from the differences, leading to the conclusion that the nth term can be expressed as TERM(n) = TERM(0) + 4*(n-1). The overall approach emphasizes identifying patterns in the differences to derive the general term expression.
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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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