10:09 LTE Done docs.google.com AA 3. * 40 points If \( f(1)=4 \) and \( f(n)=-2 f(n-1)+1 \), then \( f(4)= \) A. -7 B. 15 C. -29 D. -31 Option 1 Option 2 Option 3 Option 4 Submit Clear form Jever submit passwords through Google Forms. This form was created inside of NYC Department of Education. Does this form look suspicious? Report Google Forms

To find \( f(4) \), we start from the given information. We know \( f(1) = 4 \) and the recursive formula \( f(n) = -2 f(n-1) + 1 \). Let's calculate the subsequent values: 1. \( f(2) = -2 f(1) + 1 = -2(4) + 1 = -8 + 1 = -7 \) 2. \( f(3) = -2 f(2) + 1 = -2(-7) + 1 = 14 + 1 = 15 \) 3. \( f(4) = -2 f(3) + 1 = -2(15) + 1 = -30 + 1 = -29 \) Thus, \( f(4) = -29 \), so the answer is **C. -29**. To ensure your understanding of recursion, think about how this pattern relies on previously calculated values. It's like building a tower with blocks—each new block is based on the stability and placement of the ones below it! If you ever feel stuck with similar problems, break them down step-by-step like we did here. Often, one step at a time leads to clarity and eventually reveals the larger picture of the problem. Don't rush; each function is a story unfolding gradually!