Consider a sequence F₀₀ defined as : F₀₀(0) = 1, F₀₀(1) = 1
Consider a sequence F₀₀ defined as :
F₀₀(0) = 1, F₀₀(1) = 1
F₀₀(n) = (10*F₀₀(n – 1) + 100) / F₀₀(n – 2) for n ≥ 2
Then what shall be the set of values of the sequence F₀₀ ?
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Correct answer: (A) (1, 110, 1200)
Explanation
F₀₀(0) = 1, F₀₀(1) = 1. F₀₀(2) = (10*1 + 100)/1 = 110, F₀₀(3) = (10*110 + 100)/1 = 1200, F₀₀(4) = (10*1200 + 100)/110 = 110, F₀₀(5) = (10*110 + 100)/1200 = 1, F₀₀(6) = (10*1 + 100)/110 = 1, and the values repeat. So the set of values is (1, 110, 1200).