Determine whether the sequence is increasing, decreasing, or not monotonic.Is the sequence bounded? 6n(-3)^n

Question

I got an answer of not monotonic and not bounded. I want to make sure it's correct. Thanks.

Answer 1

6*1*(-3)¹ = -18 

6*2*(-3)² = 108

6*3*(-3)³ = -486

 

Then -18 <= 108 <= -486 is not true, and

-18 >= 108 >= -486 is not true. Therefore the sequence is not increasing or decreasing (i.e. it is not monotonic).

 

We have that 6n(-3)ⁿ > 6n > n when n is even,

and 6n(-3)ⁿ < -6n < -n when n is odd.

 

Therefore there is no M that bounds the sequence above, because taking n to be an even number greater than or equal to M we have a contradiction, and there is no N that bounds the sequence below, because taking n to be an odd number greater than or equal to -N we have a contradiction.