Answer
$ a.\quad$
Diverges.
See image. Steps given below.
$ b.\quad$
Diverges.
Work Step by Step
$a.\quad $
The steps you take will depend on the CAS you are using, but they follow the same logic.
Using the free online CAS at "geogebra.org/cas":
Cell 1: Enter the function representing the sequence
$a(x)=\sin x$
From the dropdown menu, select "Table of values".
In the dialog box for the table, set the range from 1 to 25, step 1.
When we observe the graph, the points alternate above/below the x-axis between values of y=-1 and y=+1.
The y coordinate does not seem to approach any certain fixed value.
The sequence seems to diverge.
In the next free cell of the CAS, we find the limit when $ n\rightarrow\infty$
Here, we enter "L=Limit(a, infinity)" (without quotes)
The CAS returns the limit to be " $?$ ".
(There is no limit)
$b.\quad $
The sequence diverges.
$ a.\quad$
Diverges.
See image. Steps given below.
$ b.\quad$
Diverges.
