First-order recurrence relations Quiz

1. What is the complementary function of $u_{n+1}-4u_n=7$?

• A. $A(-4)^n$
• B. $A\times7^n$
• C. $A\times4^n$
• D. $A\times4^n+7$

2. Find the constant particular solution of $u_{n+1}-4u_n=7$.

• A. $\frac73$
• B. $-\frac73$
• C. $7$
• D. $\frac{7}{5}$

3. Which trial particular solution is suitable for $u_{n+1}-2u_n=3n+1$?

• A. $\lambda$
• B. $\lambda\times2^n$
• C. $an^2+bn+c$
• D. $an+b$

4. $u_{n+1}-3u_n=4$ with $u_1=1$ has closed form $u_n=3^n-2$. What is $u_3$?

• A. $7$
• B. $25$
• C. $29$
• D. $19$

5. In an inductive proof that $u_n=3^n-2$, which line completes the inductive step?

• A. $u_{k+1}=3^k-2+4$
• B. $u_{k+1}=u_k+4$
• C. $u_{k+1}=3u_k+4=3^{k+1}-2$
• D. $u_1=3-2=1$