It is hard to understand what you mean but for "
- In a geometricsequence, 4,-2,1: find A10(i can do that) and S(sideways 8 limit thing)if it exists." I think you mean the limit at infinity, which if I'm not mistaken would be 0 (the next value is always -1/2 multiplied by the value of the preceding one, so it would get closer to zero (always twice as close as before), and switch between negative and positive

*

*
0--------*

*

kinda like that.