TS EAMCET · Maths · Functions
Let \(f(n)=A(-2)^n+B(-3)^n \forall A, B \in \mathbf{R}\) and \(n \in \mathbf{N}-\{1,2\}\). If \(f(n)+a f(n-1)+b f(n-2)=0\), then \((a+b)(b-a)=\)
- A 0
- B 5
- C 7
- D 11
Answer & Solution
Correct Answer
(D) 11
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { We have, } f(n)=A(-2)^n+B(-3)^n \\ & \qquad \begin{array}{r} f(n)+a f(n-1)+b f(n-2)=0 \\ \therefore \quad A(-2)^n+B(-3)^n+a\left(A(-2)^{n-1}+B(-3)^{n-1}\right) \\ \\ \quad+b\left(A(-2)^{n-2}+B(-3)^{n-2}=0\right. \\ \Rightarrow A(-2)^{n-2}[4-2…
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