Suppose that a sequence is defined as follows: a(1)=−3, a(n)=−2a(n-1)+10 for n≥2 List first 4?

For n=1 you are given a(n)= -3
For n=2 this means: a(n-1) = a(2-1) = a(1) = -3

Thus
a(2) = -2 * -3 + 10 = 6 + 10 = 16
a(3) = -2 * 16 + 10 = -22
a(4) = -2 * -22 + 10 = 55
a(5) = -2 * 55 + 10 = -100