Consider a sequence \(𝐹_{00}\) defined as : \(F_{00}\left ( 0 \right )= 1,…

Solution: compute the first terms using the recurrence.

1. Given: F(0)=1 and F(1)=1.

2. Compute F(2): F(2) = (10·F(1) + 100) / F(0) = (10·1 + 100)/1 = 110.

3. Compute F(3): F(3) = (10·F(2) + 100) / F(1) = (10·110 + 100)/1 = 1200.

4. Compute F(4): F(4) = (10·F(3) + 100) / F(2) = (10·1200 + 100)/110 = 12100/110 = 110.

5. Compute F(5): F(5) = (10·F(4) + 100) / F(3) = (10·110 + 100)/1200 = 1200/1200 = 1.

From these calculations the sequence cycles through the values 1, 110, and 1200. Therefore the set of distinct values of the sequence is {1, 110, 1200}.

• Distinct values: 1

• Distinct values: 110

• Distinct values: 1200