Given:

February 22, 2026

Given:

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5Question: An epidemiologist is using a model where the number of new infections each day \( I(n) \) follows a pattern based on prior days, and the recurrence is given by \( I(n) = I(n-1) + I(n-2) + I(n-3) \) for \( n \geq 4 \), with initial conditions \( I(1) = 1 \), \( I(2) = 2 \), \( I(3) = 4 \). What is the remainder when \( I(10) \) is divided by 7?
Solution: We compute the sequence modulo 7 step by step using the recurrence \( I(n) = I(n-1) + I(n-2) + I(n-3) \mod 7 \).
\( I(1) = 1 \)
\( I(2) = 2 \)
\( I(3) = 4 \)

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