**The rule for the sequence is S(n) = 2S(n-1) - S(n-2)**

**Alternative form: S(n) = S(n-1) + 3**

**Step-by-step explanation:**

In this problem, we know the first two terms of the sequence:

S(1) = 2

S(2) = 5

We are told that each term after the second is created by subtracting the term before the previous term from twice the previous term. In other words, if we call:

S(n) the current term

S(n-1) the previous term

S(n-2) the term before the previous term

This statement translates into the following sequence:

**S(n) = 2S(n-1) - S(n-2)**

Because we are subtracting the term before the previous term, S(n-2), from twice the previous term, 2S(n-1).

We can apply now the rule to find the first few terms of the sequence after S(1) and S(2):

We notice also that each term of the sequence is just equal to the previous term plus 3, so the sequence can also be written as

**S(n) = S(n-1) + 3**

Learn more about **sequences:**

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brainly.com/question/3280369

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