IGNOU BMTC 103 2026 - If the solution of the recurrence relation is , then d

Question

If the solution of the recurrence relation $u_n + \alpha u_{n-1} + \beta u_{n-2} = f(n), (n \ge 2)$ is $u_n = 1 - 2n + 3.2^n$ , then determine the values of $\alpha, \beta$ and f(n).

20 Jan 2026

Answer :

Word Count : 506

We are given the recurrence relation: [ u_n + \alpha u_{n-1} + \beta u_{n-2} = f(n), \quad n \ge 2 ] and a solution: [ u_n = 1 - 2n + 3 \cdot 2^n ] We need to find (\alpha), (\beta), and (f(n)). --- Step 1: Express (u_{n-1}) and (u_{n-2}) [ u_{n-1} = 1 - 2(n-1) + 3 \cdot 2^{n-1} = 1 - 2n + 2 + \frac{3}{2} \cdot 2^n = 3 - 2n + \frac{3}{2} \cdot 2^n ] [ u_{n-2} = 1 - 2(n-2) + 3 \cdot 2^{n-2} = 1 - 2n + 4 + \frac{3}{4} \cdot 2^n = 5 - 2n + \frac{3}{4} \cdot 2^n ] --- Step 2: Substitute into the recurrence [ u_n + \alpha u_{n-1} + \beta u_{n-2} = (1 - 2n + 3 \cdot 2^n) + \alpha (3 - 2n + \frac{3}{2} \cdot 2^n) + \beta (5 - 2n + \frac{3}{4} \cdot 2^n) ] Combine like terms: * Coefficient of (2^n):

___ _______ _____ _________ _____ _________ ___.
____ _____ ____ _______ ___ ________ ______.
____ _________ _______ ___ _________ _______ ________ ______ _______ _______ ______ ___.
___ ___ ________ _______ ______ _____ _____ _________ _____ ______.
____ ____ ______ ________ ______ __________ ____ ____ ___ ___.
_____ _____ _______ _______ _____ _______.
______ _______ _______ ____ ________ _______ ___ _______.
_______ __________ ______ _______ _______ _______.
________ __________ _______ ______ _____ ______ __________ ________ ______.
__________ _______ _________ ______ ____ __________ __________ _________.
__________ __________ ____ _________ ____ _____.
___ ______ ______ _____ ___ ____ _______ _________ ____ _______.
__________ _____ _______ _________ __________ __________ _____ ___ _________ ____ ____ _______.
_______ _____ ______ ____ ________ ___ _________ ______ ___ ________ _____.
_____ ______ _________ ______ ________.
_____ _______ ___ _____ _____ _________ ___ ______ _________.
______ ___ ______ ____ __________.
________ ______ ________ ________ ____ ____ ______ _______.
____ __________ ______ __________ ________.
___ ______ _________ __________ ________ _____ _____.
______ _______ __________ ______ ______ ______ __________ __________ ___ __________ ____.
_______ _____ ________ ________ _________ ___.
_______ ______ ___ _________ ______ _________ _______ ________ ____ ______.
______ _______ __________ ______ _________ ______ ______ _________ ________.
_____ _______ _________ ____ _____ __________ _________.
______ ____ _______ __________ ________ _________.
_____ _______ ______ ___ ____ __________ ________ _________ ______ ______.
_______ ___ ______ ____ _____ ________ __________.
_______ _______ _______ ___ ___ _____.
______ ______ _______ _____ ________ __________ _____ ___ ____ _______.
_______ ___ _________ ________ _____ _____ ________ __________ _________.
______ ____ _______ __________ ______ _____ _____.
_____ ___ ___ _________ ____ ___ ___ ___ ___ _________ _____.
___ __________ _____ _________ ___ ____ _____ __________.
____ ___ ___ _____ _________ __________ ________ ____ ____ ___ ________ ________.
___ ________ ___ ________ __________ __________ __________.
__________ _____ ______ ________ ___ ______ ___ ____ ______.
________ _________ _______ ____ ______.
_______ __________ ___ ______ _____ _______ ______ ____ ______.
___ ____ ________ ______ ______ __________ _____.
_____ _________ ____ _________ ________ ______ __________ _______ ___ ____.
______ ________ _______ ____ ____ _____ ____ _____ __________.
______ ________ _________.

IGNOU ACADEMY

Your IGNOU journey, made easier.

Solved Assignments
Study Notes
Guess Papers
Question Papers

Call Us WhatsApp

STUDY • PREPARE • SUCCEED

Skip in 10