Determine whether the sequence is increasing, decreasing, or not monotonic.

yogi55hr

yogi55hr

Answered question

2021-11-11

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
an=12n+3

Answer & Explanation

Geraldine Flores

Geraldine Flores

Beginner2021-11-12Added 21 answers

First, note that every number in the sequence is greater than zero because both the numerator and the nominator are positive integers, which means that all numbers in the sequence are larger than zero. Now, let nN be arbitrary, and let's compare an and an+1
an+1an=12(n+1)+312n+3=2n+32n+5
2n+3<2n+52n+32n+5<1an+1an<1an+1<an
The sequence will be bounded above by its first term because it is decreasing:
a1=121+3=15
Since limn12n+3=0, the sequence will be bounded below by 0.

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