I have to find maximum and minimum of a certain sequence. I was given a sequnce and have to identify maximum and minimum of this sequence:

And I think that maximum is 1 and minimum -1/2
*Speaking about maximum -> every other number of this sequence is equal or smaller and 1 is a part of sequence = OK
*Speaking about minimum -> every other number of this sequence is equal or larger and -1/2 is a part of sequence = OK
I am right?

There is a flaw in your reasoning, because you handle the two subsequences completely independently. Indeed $1$ is the largest of the decreasing sequence of terms of odd rank.
But it could be that some term of the subsequence of terms of even ranks exceeds that. This is actually not the case as this sequence is always negative, but you should not leave this implicit.
Of course, similar flaw as regards the minimum.
Also note that you use twice the expression "every other number" without specifying which.
