Determine if the sequences are increasing, decreasing, or not monotonic?

Question

an=sqrt(n+5)/(8n+5)
an=1/(4n+7)
an=(cosn)/(5^n)
an=(n-7)/(n+7)

Answer 1

The one with the cos -- i.e., the third one -- is sometimes positive and sometimes negative, and keeps changing between those states, so it's not monotonic.

The second one is the reciprocal of something that's obviously increasing, so it's decreasing.

The fourth one is easier if you write it as 1 - 14/(n+7).