**Prob.**Find the generating function for the following numeric function

a

_{r}= 7.3^{r}, r ≥ 0.
Prob. Find a*b where

ar = 3r , r ≥ 0.

br = 2r, r ≥ 0.

**Prob.**Determine the generating function of the numerical function a

_{r, }where

**Prob**. Determine the generating function of the numerical function a

_{r}, where

**Prob.**Solve the recurrence relation a

_{r}– 6a

_{r-1}+ 8a

_{r-2 }= o given a

_{0 }= 3 and a

_{1 }= 2.

Prob. Solve the recurrence relation an – 6an-1 + 9an-2 ,

With initial condition a0 = 1 and a1 = 6.
Prob. Solve the recurrence relation ar – 7ar-1 + 10ar-2 = o given that a0 = 0 and a1 = 3.

Prob. Solve the difference equation ar – 4ar-1 + 4ar-2 = o and find the particular solution, given that a0 = 1 and a1 = 6.

Prob. Solve the difference equation ar – 6ar-1 + 9ar-2 = 3, given that a0 = 0 and a1 = 1.

Prob. Determine the particular solution and general solution that satisfies the given initial condition xn – 2xn-1 = 6n; x1 = 2.

Prob. Determine the particular solution for the difference equation – ar – 2ar-1 = f(r), where f(r) = 7r.

Prob. Obtain particular ar + 5ar-1 + 6ar-2 = 3r2 – 2r +1.

Prob. Solve the recurrence relation –

ar + 4ar-1 + 4ar-2 = (r+1)2 , r ≥ 2.