recurrence relation and initial condition

Could someone make sure my answers are correct. Not sure about the first one but after the S0 s1 = 0? Here are the questions:

6.1 In the following sequences determine s5 if s0, s1, ... sn, ... is a sequence satisfying the given recurrence relation and initial condition.

a. sn= -sn-1 - n2 for n >= 1, s0 = 3

-3(3) - 33 = -9 + 9 - 0

S1 = 0

The rest of the answers up to S5 would be zero correct?

b. sn = 5sn-1 - 3sn-2 for n >= 2, s0 = -1, s1 = -2

S2 = 5(-2) - 3(-1) = -10 + 3 = -7

S3 = 5(-7) - 3(-2) = -35 + 6 = -29

S4 = 5(-29) - 3(-7) = -145 + 21 = 124

S5 = 5(-124) - 3(29) = -620 + 87 = -533

Any help would be much appreciated.