Non-decreasing sequencesI have the following sequence { n 4 − 6 n 2 }I have to determine if the sequence is non-decreasing, increasing or decreasing.In my opinion, the sequence is neither, decreasing, non-decreasing nor increasing because it seems to be increasing for all the terms except for the first and second term. Am I right or I am right?By the way,is there category for such a sequence? where you have an interval of increasing terms and one of decreasing terms or is such a sequence not even possible?

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Non-decreasing sequencesI have the following sequence  {      n    4    −  6      n    2    }I have to determine if the sequence is non-decreasing, increasing or decreasing.In my opinion, the sequence is neither, decreasing, non-decreasing nor increasing because it seems to be increasing for all the terms except for the first and second term. Am I right or I am right?By the way,is there category for such a sequence? where you have an interval of increasing terms and one of decreasing terms or is such a sequence not even possible?

bequejatz8d · Accepted Answer

Step 1The polynomial factorises as       n    2    (      n    2    −  6  )  ,, which vanishes somewhere between   n  =  2 and   n  =  3 if we for the moment think of n as a real variable. It then increases afterwards. Thus, you&#039;re right that it cannot be monotonic.Step 2Sequences that are not monotonic may generally be classified as oscillating.

hifadhinitz · Accepted Answer

Step 1Let       a    n    =      n    4    −  6      n    2  Step 2then       a          n      +      1        −      a    n    =  (  n  +  1      )    4    −  6  (  n  +  1      )    2    −  (      n    4    −  6      n    2    )  =  …

I have the following sequence {n^4-6n^2}. I have to determine if the sequence is non-decreasing, increasing or decreasing.

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