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Explicit recurrence solutions, equilibria and population models

Question 1 of 8

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The recurrence holds for every nonnegative integer index. Its multiplier is nonzero. Values are exact

\[u_{k+1}=\left(-2\right)u_k+\left(-2\right),\quad k\ge0\]
\[u_0=4\]
1 mark

Find the equilibrium value L satisfying L=rL+c. Give an exact value. Integers, fractions and exact terminating decimals are accepted