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Subtract 3 from both sides to bring all terms to one side:
Question: A geneticist models the expression level of a drought-resistant gene as a function $ f(n) $ satisfying $ f(n + 1) = 3f(n) - 4 $, with $ f(1) = 5 $. Find $ f(5) $.
f(2) = 3f(1) - 4 = 3(5) - 4 = 15 - 4 = 11
f(3) = 3f(2) - 4 = 3(11) - 4 = 33 - 4 = 29
f(4) = 3f(3) - 4 = 3(29) - 4 = 87 - 4 = 83
f(5) = 3f(4) - 4 = 3(83) - 4 = 249 - 4 = 245
We compute each term using the recurrence: