The sequence given is defined using a recursion formula. Write the first four terms of the sequence. \[ a_{1}=4 \text { and } a_{n}=2 a_{n-1}+1 \text { for } n \geq 2 \]

Step 1 ：The sequence is defined recursively, meaning each term is defined based on the previous term.

Step 2 ：The first term is given as 4.

Step 3 ：The second term can be found by substituting n=2 into the recursion formula, which gives \(a_2 = 2*a_1 + 1\).

Step 4 ：The third term can be found by substituting n=3 into the recursion formula, which gives \(a_3 = 2*a_2 + 1\).

Step 5 ：The fourth term can be found by substituting n=4 into the recursion formula, which gives \(a_4 = 2*a_3 + 1\).

Step 6 ：Final Answer: The first four terms of the sequence are \(\boxed{4, 9, 19, 39}\).