Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Our platform provides a seamless experience for finding reliable answers from a knowledgeable network of professionals. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

three terms of an arithmetic sequence are shown. f(1)=3, f(3)=6, f(7)=12 what recursive formula could define the sequence ? A. f(n+1)=2f(n) B. f(n+1)=f(n)+3 C. f(n+1)=f(n)+1.5 D. F(n+1)=0.5f(n)

Sagot :

kate200468
[tex]an\ arithmetic\ sequence:\\\\ d\ \ \rightarrow\ \ the\ difference\\\\f(n)=f(1)+(n-1)\cdot d\\\\f(n+1)=f(1)+n\cdot d\\\\f(n+1)-f(n)=f(1)+n\cdot d-[f(1)+n\cdot d- d]=\\\\=f(1)+nd-f(1) -nd+d=d\\\\\Rightarrow\ \ \ f(n+1)=f(n)+d[/tex]

[tex]f(1)=3\ \ \ and\ \ \ f(3)=6\\\\f(3)=f(1)+(3-1)\cdot d\ \ \ \Rightarrow\ \ \ 6=3+2d\\\\ \ \ \Rightarrow\ \ \ 2d=3\ \ \ \Rightarrow\ \ \ d=1.5\\\\ f(n+1)=f(n)+d\ \ \ \Rightarrow\ \ \ f(n+1)=f(n)+1.5\\\\\\Ans.\ \ \ f(1)=3\ \ \ and\ \ \ f(n+1)=f(n)+1.5[/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.