(4) Terms of a sequence can also be complex numbers. All the usual rules and formulae apply.

a. If the first term of a geometic sequence is i and the common ratio is r=2i, list the first five terms of this sequence and find their sum.

b. Identify r and find the sum of this infinite geometric series:

27+(-9i)+(3i^2)+(-i^3)+((i^4)/3).....

(5)

a. There is a sequence u with an associated series S, and all we know is that S(n)=n^3. Is the sequence u arithmetic, geometric, or neither?

b. Find a formula for u(n), the nth term of the sequence. Hint: S(n)=S(n-1)+u(n)