You found out that k is 3/2.
So if you look at the first 4 terms, you can clearly see a pattern of 1, -1/2, 1, -1/2 and so on.
You need the sum of the first 100 terms. Which means, a half of those will be 1s, and the other half will be -1/2s. Thus, 50*1+50*(-1/2)=50-25=25.