Number cell puzzle Method

Is there a methodical way to answer a question like these without using trial and error.
'The empty cells are filled by adding the two preceding numbers' The first ones are straight forward but then they get a little trickier.e.g.
-15,_,_,_,-27 and -6,_,_,_,3
Very much appreciated for any simplified method.

Let's use variables instead of blank spaces: -15, x, y, z, -27. From the problem description ("The empty cells are filled by adding the two preceding numbers") we know that there's a certain kind of relationship between all these numbers. Let's put those relationships in equation form:

(1) y = -15 + x
(2) z = x + y
(3) -27 = z + y

Let's substitute y from (1) into (2):

(1) y = -15 + x
(2) z = x + (-15 + x) ↔ z = 2x - 15
(3) -27 = z + y

Note that both (1) and (2) involve only x on their right hand side. Let's take advantage of that fact. We substitute y from (1) and z from (2) into (3) and then solve (3) for x:

(1) y = -15 + x
(2) z = 2x - 15
(3) -27 = (2x - 15) + (-15 + x) ↔ -27 = 2x - 15 - 15 + x ↔ -27 = 3x - 30 ↔ 3 = 3x ↔ x = 1

If x = 1, then from (1) y = -14 and from (2) z = -13.

So we have arrived at the following sequence:

-15, 1, -14, -13, -27

Let's test this against the conditions we were given:

-14 = -15 + 1 Checks out
-13 = 1 + (-14) Checks out
-27 = -14 + (-13) Checks out

I hope this helps

Adding 2.25 will work.

-6, -3,75, -1.5, 0.75, 3