Question 2739 – UGC NET CS 2017 Jan -paper-2

Given data,
Sequence F​ ₀₀​ defined as
F​ ₀₀​ (0) = 1,
F​ ₀₀​ (1) = 1,
F​ ₀₀​ (n) = ((10 ∗ F​ ₀₀​ (n – 1) + 100)/ F​ ₀₀​ (n – 2)) for n ≥ 2
Let n=2
F​ ₀₀​ (2) = (10 * F​ ₀₀​ (1) + 100) / F​ ₀₀​ (2 – 2)
= (10 * 1 + 100) / 1
= (10 + 100) / 1
= 110
Let n=3
F​ ₀₀​ (3) = (10 * F​ ₀₀​ (2) + 100) / F​ ₀₀​ (3 – 2)
= (10 * 110 + 100) / 1
= (1100 + 100) / 1
= 1200
Similarly, n=4
F​ ₀₀​ (4) = (10 * F​ ₀₀​ (3) + 1₀₀) / F​ ₀₀​ (4 – 2)
= (12100) / 110
= 110
F​ ₀₀​ (5) = (10 * F​ ₀₀​ (4) + 100) / F​ ₀₀​ (5 – 2)
= (10*110 + 100) / 1200
= 1
The sequence will be (1, 110, 1200,110, 1).