I'll go over part (b) only
Answer: 31
Reason:
The terms are 1, 4, 4^2, 4^3, ..., 4^30.
Rewrite some of the terms so we have a base of 4 each time.
1 = 4^0
4 = 4^1
We get the slightly updated equivalent sequence 4^0, 4^1, 4^2, 4^3, ..., 4^30. Then from there we focus on the subsequence of exponents 0,1,2,3,...,30. There are 30 whole numbers from 1 to 30 when including both endpoints. We add on 1 because of the zero up front. So we have 30+1 = 31 values total in the set {0,1,2,3,...,30} and 31 values in the set {4^0, 4^1, 4^2, 4^3, ..., 4^30}