Second-order recurrence relations

Second-order recurrence relations Quiz

Spec 6.2 · Edexcel A-Level Further Maths: Quiz

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  1. 1. Find the roots of the auxiliary equation of un+2−7un+1+12un=0u_{n+2}-7u_{n+1}+12u_n=0.

    • A. 33 and 44
    • B. −3-3 and −4-4
    • C. 22 and 66
    • D. 77 and 1212

  2. 2. What is the general solution of un+2−4un+1+4un=0u_{n+2}-4u_{n+1}+4u_n=0?

    • A. A 2n+B(−2)nA\,2^n+B(-2)^n
    • B. A 4n+BnA\,4^n+Bn
    • C. (A+Bn) 2n(A+Bn)\,2^n
    • D. A 2n+B 2nA\,2^n+B\,2^n

  3. 3. Find the particular solution of the form un=λu_n=\lambda for un+2+un+1+un=9u_{n+2}+u_{n+1}+u_n=9.

    • A. 99
    • B. 33
    • C. −3-3
    • D. 13\frac13

  4. 4. un+2=un+1+2unu_{n+2}=u_{n+1}+2u_n, u1=3u_1=3, u2=3u_2=3. The roots are 22 and −1-1. Find AA and BB in un=A 2n+B(−1)nu_n=A\,2^n+B(-1)^n.

    • A. A=1, B=1A=1,\ B=1
    • B. A=2, B=−1A=2,\ B=-1
    • C. A=1, B=−1A=1,\ B=-1
    • D. A=−1, B=1A=-1,\ B=1

  5. 5. For un=A(0.3)n+B(0.6)n+10u_n=A(0.3)^n+B(0.6)^n+10, what happens as n→∞n\to\infty?

    • A. grows without bound
    • B. tends to 00
    • C. tends to 0.90.9
    • D. tends to 1010

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