how that an = 2n+1 is a solution to the recurrence relation an = 2an-1-1 with a₁ =3.

4. Find an explicit formula for the recurrence relation an= An-1+6an-2 ao= 5 aj = 0 %3D

13. Solve the recurrence relation. Given:a0=3 a1= 6 an= 6a n-1 + 7a n-2 Show your work in the space provided. a. Find c1 and c2  an= (6)a n-1 + (7)a n-2 c1=  c2=    b. Substitute c1 and c2 into the following equation:  r^2- c1r - c2= 0  show your work here:     c. Identify a, b, and c in the quadratic equation. a=  b=  c=  d. Use the quadratic formula to find the two roots. Here is the quadratic formula: -b + Vb^2- 4ac/2a Show your work here: e. Substitute two roots, r1 and r2 into the equation an= a1r1^n+ a2r2^n Show your work here:     f. Now substitute to find two equations, a0 and a1 Remember to use the equation you found from step e. show your work here: a0= 3 =a1= 6 = g. Add the two equations together find a1 and a2  a1=  a2=   h. What is the solution to the recurrence relations? an=    i. Find the 10" term of the sequence, using the solution to the recurrence relation you just found. Show your work here:  a10=

5. Solve the recurrence relation an = 3an-1- 2an-2 with initial conditions ao = a, a1 = b. Here a and b are constants. Зап-1 — 2ап-2 %3D