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Sum of Sequence

Source: 1994 National High School Mathematics League, Exam One, Problem 3

February 28, 2020

Problem Statement

Sequence (an)(a_n) satisfies that 3an+1+an=4(n≥1),a1=93a_{n+1}+a_n=4(n\geq1),a_1=9, let Sn=∑i=1naiS_n=\sum_{i=1}^{n}a_i, then the minumum value of nn such that ∣Sn−n−6∣<1125|S_n-n-6|<\frac{1}{125} is (A)5(B)6(C)7(D)8\text{(A)}5\qquad\text{(B)}6\qquad\text{(C)}7\qquad\text{(D)}8
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