Can't solve a sequence (to determine if a given value is a member)

[theakdad]

An arithmetic sequence has the property:

\(\displaystyle a_{n+1}-a_{n}=d\)

While a geometric sequence would have the property:

\(\displaystyle \frac{a_{n+1}}{a_{n}}=r\)

Note: Both $d$ and $r$ are constants that do not depend on $n$. Does this sequence satisfy either property?

It seems its arthmetic

 

[MarkFL]

It seems its arthmetic

I find:

\(\displaystyle a_{n+1}-a_{n}=\frac{(n+1)^2+1}{2(n+1)^2}-\frac{n^2+1}{2n^2}=-\frac{2n+1}{2n^2(n+1)^2}\)

Thus, the difference between two succeeding terms is a function of $n$, and so the sequence is not arithmetic.

 

[theakdad]

I find:

\(\displaystyle a_{n+1}-a_{n}=\frac{(n+1)^2+1}{2(n+1)^2}-\frac{n^2+1}{2n^2}=-\frac{2n+1}{2n^2(n+1)^2}\)

Thus, the difference between two succeeding terms is a function of $n$, and so the sequence is not arithmetic.

Ad its not geometric?

 

[MarkFL]

And its not geometric?

What do you find when you compute the ratio I gave above?

 

[theakdad]

What do you find when you compute the ratio I gave above?

Will try tomorrow,im litlle busy now