Limit of a recursively defined sequence

Hey

The problem is:

a(n+1) = ( a(n)^2 +16) / ( 2a(n) + 6) converges to the limit:...?

for n>=1 and a(1) = -10

Also note (n+1) and (n) are subscripts

If someone could solve this and explain what they are doing it would be extremely helpful. My textbook has no questions like this so I'm completely lost.

Also another question..:

If f(x) is a function that is 8 times continuously differentiable such that the coefficient of x^5 in its 8th MacLaurin polynomial is 0.2, then f^5(0) =

Help would be much appreciated =)