what is the relationship between the terms? is there a common difference? a common ratio? neither? let's see.
to go from 4 to -6 you would subtract 10. but subtracting 10 from -6 gives -16, which is not the third term. so there is no common difference.
what about a common ratio?
is it true that 6/4 = 9/6 = 13.5/9 ? YES!
what are these ratios equal to? 6/4 = 9/6 = 13.5/9 = 3/2
so that is our common ratio, which means this is a geometric sequence.
so the formula for this sequence will be of the form ar^(n-1), for n = 1,2,3,4,5...
where a is the first term, r is the common ratio. so obviously, this would be:
4(3/2)^(n - 1)
but wait! what about the changing sign? do we just add (-1)^(n-1) as you suggested? well we could, or we could just change the common ratio to a negative. so
a_n = 4(-3/2)^(n-1)
try the same analysis for part c, see what you come up with. and what type of sequence is a?