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If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2}-a x+b=0 \) and \( A_{n}=\alpha^{n}+\beta^{n} \), then which is true?
(A) \( A_{n+1}=a A_{n}+b A_{n-1} \)
(B) \( A_{n+1}=b A_{n}+a A_{n-1} \)
(C) \( A_{n+1}=a A_{n}-b A_{n-1} \)
(D) \( A_{n+1}=b A_{n}-a A_{n-1} \)
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