Question

Determine the monotonicity of the sequence if (an) satisfies the equality (an+1)-(an)=-3 for all n.

Answer 1

$$a_{n+1}-a_n=-3, n\in \N$$

$$a_{n+1}=a_n-3, n\in \N$$

Then

$$a_{n+1}<a_n, n\in \N$$

The sequence $\{a_n\}$ is strictly decreasing sequence =>decreasing sequence => monotonic sequence.