`a_n=(-2/3)^n=(-1)^n(2/3)^n={(-(2/3)^n if n=2k-1),((2/3)^n if n=2k):}`

This tells us that odd-numbered terms are negative, while even-numbered
terms are positive. Since the terms alternate in sign, the sequence is
alternating. In other words, **the sequence is** **not
monotonic**.

All terms of the sequence are in `[-2/3,4/9].`

This is because `-(2/3)^n< -(2/3)^(n+1),` `forall n in NN` and `lim_(n to infty)-(2/3)^n=0`

Also, `(2/3)^n>(2/3)^n,` `forall n in NN` and `lim_(n to infty)(2/3)^n=0`

Clearly `-2/3` is the smallest term of the sequence and `4/9` is the greatest.

Therefore, **the sequence is bounded**.

The image below shows the first 20 terms of the sequence. We can see that the sequence is also convergent even though it is not monotonical ` `

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