First-order recurrence relations Quiz

1. $u_{n+1}=3u_n$ with $u_1=2$. Find $u_n$.

• A. $2\times3^{n}$
• B. $3\times2^{n-1}$
• C. $2\times3^{n-1}$
• D. $6^{n-1}$

2. Find the particular solution of the form $u_n=\lambda$ for $u_{n+1}-2u_n=6$.

• A. $6$
• B. $-6$
• C. $3$
• D. $-3$

3. What is the general solution of $u_{n+1}-2u_n=6$?

• A. $A\times2^n-6$
• B. $A\times2^n+6$
• C. $A\times(-2)^n-6$
• D. $A\times6^n-2$

4. In the previous question $u_1=4$. Find $A$.

• A. $2$
• B. $3$
• C. $4$
• D. $5$

5. Describe the long-term behaviour of $u_{n+1}=0.5u_n+3$.

• A. tends to $3$
• B. tends to $6$
• C. grows without bound
• D. tends to $0$