14, 9, 4, -1, -6, ...
Note that, for example, the third term is 10 less than where we started. The fourth term is 15 less than where we started, the fifth is 20 less, and so on. Continuing this pattern, the, say, 100th term would be 495 less than what we started with (99 * 5 = 495). So, the nth term is going to be, basically, the first term minus 5*(n-1). So the nth term will be 14 - 5*(n-1), or, if you simplify, 19 - 5n. (Note that this is assuming we consider 14 to be term #1 - sometimes it is considered to be term #0, resulting in the much nicer formula 14 - 5n. Make any adjustments necessary based on your class, but this should get you the general idea.)
-12, -15, -18, -21, -24, -27.
So the common difference is -3. Now, we need to work backwards from term 10 to get back to the first term. Since the common difference is -3, but we're working backwards, we need to add 3 each time. The 9th term, then, will be -9, and so on. Keep going back as far as you need to.
The second term, then, will be 16 * (1/2), right? (Or, simply, 8).
The third term will be half the second term, or 16 * (1/2) * (1/2) = 16 * (1/2)^2. (Or, simply, 4).
The fourth term will be half the third term, or 16 * (1/2)^2 * (1/2) = 16 * (1/2)^3. See a pattern developing?
Really, the only thing changing is the exponent to 1/2. How does the exponent relate to which term we're on? Once you figure this out, what will the exponent be if the term # is a general one, like n?
Hope this helps! Your text probably has formulas for many of these things, but ultimately understanding WHERE the formulas come from, which is what I tried to explain above, is a lot more useful than just memorizing the formulas, which can be tricky.